Just to fill in a potential blank, any connection longer than 4 hours on a same-day domestic itinerary is considered a stopover. Unless there is a fare that allows free stopovers, the price would be increased, either because of a charge within the fare for stopovers, or because it would have to be priced as two separate fares. (Though in practice you don't really need to concern yourself with this detail.)

Because the schedule requires the stopover, you have to use the multi-city search on AA.com.

And then frankly, I'm pretty precious myself, but TPA-LAX is not that long of a flight, and the regular first class seats are plenty spacious -- totally not worth doubling the travel time (and cost?) to get a flat bed via MIA. In my opinion of course.