No SBR's? Well, that rules out the 607 or 609/XM177 Commando.
There is still the XM177E2 which can be done very well in a non SBR configuration. It also seems to be the most popular and the lack of the need for a tax stamp probably contributes to that.
I'm also a big fan of the 603/613/M16A1 rifle. That is the configuration which served the Armed Forces for the greatest length of time.
Another option would be the 605 if you wanted something shorter and still non NFA. If the flash hider is permanently attached it meets the minimum length requirement. You could just build another upper for your 604 lower to do this one. There's no rule saying that you have to build complete rifles. You can have multiple uppers too.
With NDS making lowers and now uppers in both slick side and forward assist configurations it is easier than ever to just build what you want as far as retro builds go.
For the XM177E2 you would need an NDS16A1 lower and NDS A1 upper to start with.
I, and others, would highly recommend the Essential Arms XM177 style stock. It has a shiny black finish that is a virtual clone of the original. The profile is almost exactly the same.
Your choice of barrel would be limited to the Bushmaster lightweight profile, a Colt (preferably a modern one, not an original early one), or CMMG lightweight profile. The lightweight profile is the correct one. There may be some others on the market but I would make sure that it worked before incorporating it into the build. Chrome lining is not only correct, but very desirable. I'll let the rest of the gang make their recommendations on who to have the barrel work done by.
The remaining parts are off the shelf and still available. You might have to search a little harder to find a lower parts kit with a no notch selector. The bolt group is the standard notched parkerized unit. You'll want an A1 grip and six hole handguards.
That's the quick and simple version of it.
XM177E2
605
603/613/M16A1
Sooner or later you will end up in BRD rehab. It's only a support group and it really doesn't encourage quitting.