275/35/18 front and 305/30/18 rear on a stock '69 Chevelle?
 

These are the tire sizes I'm proposing to run on my '69 Chevelle project.
R888 or NT01 tires are my first choices for it.

With custom wheels will these fit on my car? I have the stock wheel tubs and frame rails. The rear body 1/4 panel lips look like they could easily provide another 1/2" of clearance if they were heavily rolled.

When I bought the car it had a 325/50/15 M/T ET street drag radial on a 15x10 rim that did clear when rolling on stock wheel lips... but I never drove on them as the car has yet to run in my possession.
I'm thinking an 18x9 front and 18x10 rear.

These are all widths from the M/T tire I was talking about p/n 3757R -
rim 10"
sidewall 13.1"
tread 11.6"
diameter 28"

Do I need additional mods to the rear to fit this size tire aside from a heavy wheel lip roll? I haven't really gotten a clear answer and my car is at the fabrication shop so any further surgery could be done if needed. Suspension out back will be custom JRi coilovers, TRZ upper/lower control arms. I may add a Panhard rod to keep the rear axle centered. A Watts linkage would really impact exhaust clearance as I'm running a single 4" off the turbo into an e-cutout, then dual 3" into 4 mufflers all the way back.

305 will fit if the wheel is built perfectly. You have plenty of width back there. You can get over 1/2" if you trim/roll the fender lip. The biggest problem with these cars is the lower shock mounts. They are at an insanely steep angle outward, and really limit wheel width. If you've modded the rear suspension, it's not an issue. My car measures 14" from my trimmed outer fender, to inner fender. I can get an 11" wheel back there no problemo. Stock tubs.
275 on front is a go, as long as your control arms allow wheel width at full lock. My Global West units will let me get a 9.5" or maybe even a 10" wheel up front if I wanted.

Thanks for the input! Good call on the lower shock mounting points. Will remind my fabricator about that.
I have Global West front tubular A-arms also.

What would it take to fit an 18x12 and 335 out back? I assume modify the frame rail and mini tub?

Yes sir, the tubs and frame rail would have to move inward. This is doable yourself, or there are kits out there. ABC Performance offers one.
I have seen guys pull the quarter outward to gain an inch or so, also.