Definitely pick JVC over Sony.
Do NOT get a screen that's more than a couple thousand dollars. Stewart is up towards the top, but a DaLite screen with HD Progressive material in .9 gain or so is an excellent option.
I'm not sold on your in-wall choices, but so be it.
Using your phone as a remote control sucks. PERIOD. A tablet isn't much better.
WHY?
First, your phone isn't always with you when you are in your home. So, that makes it a crap option. If you have it upstairs on your charger, then it's no good to you in the theater.
A tablet that is dedicated is at least there all the time.
But, a tablet sucks as well.
WHY?
Because the interface to control your cable box is up on the screen in front of you, not on the tablet in your lap. You can't easily use a smooth screen for tactile navigation. Up/down/left/right/enter, channel up/down, volume up/down, etc. These are all easy buttons to memorize on a remote control, but with a smooth surface touch screen, you must look down at the screen to use it. But, the channel is up in front of you. The guide is up in front of you. The volume feedback is up in front of you. Absolutely nothing you need is displayed on the tablet, it's all on screen.
You WANT a tactile remote control with hard buttons that you can memorize. Yes, it can be incredibly simple to use. A single button that says "Blu-ray" or "Cable" or "Roku", etc. One touch, the projector turns on, the receiver powers on, everything switches to the proper input, etc.
Projector and screen should be no more than about $10,000.
Be aware that if you are having this installed for you, then that's going to eat into budget. If this is a finished space, then in-wall cabling is recommended. You will need to pick an equipment location, and may need a proper cabinet/rack for the gear (budget). If walls are up, then holes will be made, those will need to be repaired, and the room painted appropriately. That will be part of budget. While you do have a very solid budget for a very nice system, there are many directions it will need to go, so breaking down fixed costs first is a good plan.
I would start with the room design. Where are you going to sit? How far from the screen? Do you want two or one row of seating? Plan on painting walls DARK as well as the ceiling. If you already have lights installed, you may want to rework them so that they are appropriate for theater use. Zoned lighting with spotlighting over seating areas is strongly recommended. Then a lot of lighting in the rest of the space to compensate for the dark walls, ceiling, and carpet. If you have light carpet, plan to replace it with dark carpet. If it is all hardwood surface, plan on a dark area rug to reduce brightness of both audio and reflected light in the room.
Quickly a budget that may have sounded like $30,000 for speakers can become $20,000 because of other items which are potentially more important to the setup of a proper home theater space.
But, stick with JVC and do NOT spend more than a couple thousand dollars on a fixed frame screen. In a good room, a $500 screen will outperform a $5,000 screen in a poor room.