I'm sitting in the middle here: I don't think OP is utterly nuts for wanting to do a trip. I think the timing is still a little bit lousy for it (I'd probably shoot for June, personally).

As to the exposure risks, I'd suggest that you need to consider both sets of risks: That you have the virus but are asymptomatic/pre-symptomatic, and that you might pick up the virus on the trip. The former involves a very frank inventory of your contacts over the last few weeks prior to the trip date (and I don't mean "Eh, nobody I know picked it up"...really go through and analyze how much you have been out and about, possible contact points for picking it up, and so on). The latter involves your plans on the trip, whether you can arrange hotel rooms with an extra "stay buffer", and so on. Basically, you're not only analyzing your own risk tolerance but what sort of a risk you might present to others.

To go to a farcical extreme, if you've literally been living in a cabin in the woods for the last few weeks with no human contact whatsoever your risk of carrying the virus with you "on the way out" would be damned near zero. On the other hand, if you're an "essential worker" with a customer-facing position and a lot of customer traffic, do not pass go, do not collect 200 SkyPesos. And there's everything in the middle (e.g. you've been working from home and in a state of quasi-isolation).

As a personal example: At the end of March I went to Florida. I too Amtrak, sequestered myself in my roomette (except for breakfast on the way into Florida), and effectively only had contact with a specific group I was meeting with down in FL. I had incidental contacts with a Lyft driver between Amtrak and the airport/a taxi driver on the return and the car rental agent (though I maintained distance except for the exchange of keys in the latter case). Everyone else in the group I met with had done the same. Prior to the trip my contacts had been extremely limited in the previous two weeks (I did have dinner out twice in the preceding two weeks, but those dinners were right at the start of the two-weeks-pre-trip period). Other than that, my only contacts had been at the window of various fast food places/well-distanced trips to a 7-11 and otherwise within an established isolation unit. Upon returning home I did not visit the third member of my isolation unit for two weeks (since while I was away, he figured out that he was in a high risk population...we had a "chat" about the timing of this since he was part of the discussion where I chose to take the trip and I confess that I wasn't amused when he tried to deflect with "I'm not your mother" when I was wrangling with how to make the trip while we were eating dinner the night before I left). The three of us (and the folks in FL) judged that this plan presented an exceedingly limited risk of transmission "either way" (me to others on the trip, me to people back home upon return), though the third member effectively had a change of circumstances (prior to this, part of the analysis was no close physical exposure to anyone in a high-risk group on anything resembling a sustained basis). I took the train instead of flying (despite walk-up fares being about $20 each way RIC-MCO on B6 at the time) as a risk mitigation measure (the load factors on several flights I looked at were too high for my comfort...a flight with only 10 pax on it is something I would have considered, but there was substantial crowding on at least one leg of most itineraries; by contrast, I basically had a car to myself on the train).

Similarly, I went through great pains to arrange a massage this month. Again, we had a detailed analysis of the risks involved (it was a one-day trip, no overnights/hotels involved, the therapist wasn't seeing clients otherwise and hadn't been for some time so he presented at most a negligible carrier risk, and even my high-risk friend not only agreed that the myofascial work was a reasonable medical item [particularly considering how sedentary I've been in the last few weeks] but would have arranged for a massage of his own if the therapist had come to me instead of me going to him [the relevant travel fee would have been excessive]. On my end, I'd been "back in the bubble" for just under three weeks, so my risks for transmitting out were damned near zero. But, again, we all basically had about a five-way conversation in which we detailed our gameplan and possible exposure risks so that the high-risk member of my "party" had his eyes open, and he held/holds something very close to an absolute veto.

So, ask yourself questions like I did above if you really want to take a trip. Consider where you'd be going, consider your hotel/food situation, and so on. But I would argue that the questions you need to ask aren't a 30-second "Is this a good idea?" thought exercise but something that requires a serious discussion with, bluntly, various stakeholders in your life (mainly folks you're in close contact with but also your job).

The bottom line, however, is that it is entirely possible to carry out an analysis like this and come back with "Yes, the risks are acceptable". A large part of the reason that the shutdown/stay-at-home orders are in place has to do with people simply not carrying out anything resembling this analysis. This also has to do with why I think Sweden is handling things differently (there's greater compliance with "strong recommendations" there).

As to OP's trip, if he's dead set on it, I would advise reversing it and driving DC-Seattle and planning to be relatively isolated for two weeks upon return (I realize there are likely practical limits to this). Taking the presumption that the "airport experience" represents the largest risk to the whole enterprise, I'd say that moving that to the end (where you're not going to accidentally play Typhoid Mary on your way home) would help with that concern.

I'd also advise planning the trip and taking into account the various circumstances along the road (e.g. hotels, food options, and so on). There are some routes through parts of the West where OP might have the option to actually sit down at a restaurant for a meal, and what OP would want to do as far as that goes should be considered in advance.

So do I think OP is nuts? I do not. But I do not necessarily think that OP has weighed the tangle of factors at play here, either.

[As an aside, there's no way I'm going to be able to stick with staying at home 12-24 months. I'm politely putting an outer edge on this at sometime in June or July [VA's orders presently expire at the start of June], since in some respects my sanity is starting to fray just a little around the edges right now, and that's with putting a healthy side of taking my classic Cadillac out for a cruise [the local Costco wipes the pump handles between each transaction, so I think the transmission risks there are negligible]. Similarly, I very strongly doubt I'm going to be able to get my brother to "back off" of DragonCon [or whatever happens to be in Atlanta over Labor Day weekend]...but we're going to negotiate pre-con/post-con plans and protocols with with the third person in our group, and those will depend very much on the prevailing circumstances at that point.

Edit: I also think the point about "stopping in small[er] towns" is worth weighing, given the contact points. I would advise considering that when planning out where you expect to stop.