I just cut some shim stock, drill a hole and place under the base. I prefer one piece base so that you maintain alignment easier. Done the two base thing for years. Now older, wiser and lazier.
Looks good. Leave the steel/wire in there. Bedding will break down under vibration. Same reason you put rebar in concrete.
At present my 223 doesn't have any bedding compound and it is working just fine.
Consider getting some Burris rings w/ inserts. I see you are using solid rings. Not so good for your scope health unless your base alignment is bang on. Plus you can gain another 20mins of up by using the inserts - 30mm rings I presume.
I also see that the front has a huge gap and the rear looks flat. You want to cant the bases so that a straight across both bases leaves no gaps. Raising it alone will cause the scope rings to be way out of whack and bend the scope.
That's just a thought and may not be correct as the pic shows.
Jerry