April is always really busy. It's Sakura season. It's definitely high season. Fall is popular too, though to a lesser extent. Summer (hot and humid) and winter (cold and rainy) are the less popular, cheaper times.

HR availability has been strange lately. They will show that they are sold out and then a few days later they will show that there cheap rooms available. I have no idea what's going on. But I'll bet that if you keep looking, you can find availability between now and then.

If you are ok with something the quality of the HR (nice, but not luxury) then I would suggest that you check back every week or so because you can probably save a lot of money over what you are going to pay at PH. Of course you can still book PH in the meantime, but there's always the option to cancel and rebook elsewhere.

Personally I would choose location over breakfast every time. This is not like lounge breakfast in the US; it's actually good. And as I said, there's always the Privé option so there's no reason you can't have both. You still get all your status benefits and earnings with Privé; the only downside is that you are paying standard rate instead of member rate. I've gone through Kristen Nix for Privé bookings before (she is probably the first TA who will show up if you search for Privé Travel Agent) and she was great (but most travel agents can book these rates)

If restaurant breakfast instead of lounge breakfast is important to you in general, I would suggest using Privé a lot (not just for this trip). I think that you will find that it gets you exactly what you are looking for for either the same price, or slightly more (and sometimes slightly less)