I have 7 bikes currently, 5 of them DIY ebikes. It's been a great journey thus far and thankful to my friends on EBR this summer since I joined.
I understand the draw to Mid-Motor with a belt drive, perhaps a 3 or 5 speed hub in the rear. I haven't tried mid motors (yet) as I have had fantastic luck with RWD and 2WD Hub setups. If you end up building a belt drive Mid Motor setup, please please do share it here for us to see how you make out with it.
Integrated battery was never something I looked for. Downtube batteries work great. On some bikes I have a pair of bottle holders strapped together near the stem (road going bikes) and for my off road bikes I just used a camelbak for hydration. I'm guessing you want the integrated battery to have bottle mounts in the triangle? If yes, these are much easier to move or go with a camelbak then trying to get an integrated battery mount for a DIY project.
The first DIY bikes I started with were various models pre-built with Bionx that I in turn upgraded/fine tuned. I'm thankful to have experienced them. While I still love these bikes and what they meant to me, I'm in the process of parting them out and selling them off this fall/next spring.
I'm doing this as I learned what I really liked and have 3 final DIY bikes I'm building this year (full details to come). One just for speed, one for long distance road riding with multiple batteries and one fat tire bike for dirt/mud/snow riding.
What I found as a great starting point to look for (new and used) for DIY builds is the bikes from Surley.
Serious Steel Bikes for People Who Don't Take Themselves Too Seriously
surlybikes.com
They are so strong and overbuilt from the frame out it makes adding as much (or as little technically) power you want to them easy. 2 of my final 3 bikes are Surley's and both are 2WD builds. The Surley front forks are the only ones I trust from an OEM provider to take a front hub motor for my 2WD setups.
You want to squeeze 5" tires in? 4.8" for sure will fit in the Surley Ice Cream Truck, previous years they sold the MoonLander, Maybe the Pugsley, etc. Have a look if you have the time.
On a final note, I have a KHS500 (basic fat bike) with 4.8 tires that came with a 170mm Bionx D motor setup, 500watts nominal RWD. It absolutely is my 'go anywhere' bike. Rides ok/fine on road, loves all type of dirt, mud and snow. If I'm ever exploring an area/trail/path for the first time - I always take it first to scout out what I'm riding on before I perhaps take one of my other bikes.
While I'm selling this bike off, it's only because my Surley Pugsley with 3.8" Nate tires will be a good replacement for it except for anytime I have to ride on road (rides and sounds like a tractor, lol). Anything 3.8" and up to 5.0" with the tread you choose best for you will be a great fit.
Just some thoughts from a 2 year DIY club member, hope this helps.
Cheers
Shaun