Can you slide the existing crossmember back a few inches, perhaps even reuse some of the rivet holes.

Some pictures would help further the discussion.

In my opinion if the frame wasn't welded when new then do all you can to avoid welding on it now.
Welding may be the easy way out but fully understanding the stresses and compromises involved is above my pay grade. Therefore I'll trust the engineers that designed that frame and so many after it, general rule is don't weld on a riveted or bolted frame, I'm sure they have good reasons.

I have welded on frames before though... To repair them where no other option sort of replacement existed. One was a 1928 Hudson car that some time long long ago was wrecked and two frames pieced together front to back but welded very poorly. They even laid an old carriage bolt in the bottom flange to fill a gap and welded right over top of it. That one I cut out the bad/questionable areas and slipped new pieces of frame in with proper clean welds. When done it looked as if nothing ever happened. Another was a 60's Chevy truck someone had cut and welded on the bottom flange of the frame just behind the front crossmember, probably trying to fit some exhaust. This modification caused it to crack and it traveled well up the web of the frame and in a short time the frame would have folded up, would have been the end of the truck.

What you're looking at I think could still be done without welding and may avoid some of the risk that welding brings to a frame. Not to say that drilling and bolting doesn't bring it's own risk but they seem easier to understand.

•1951 GMC 250 in the Project Journals
•1948 Chevrolet 6400 - Detroit Diesel 4-53T - Roadranger 10 speed overdrive - 4 wheel disc brakes
•1952 Chevrolet 3800 pickup
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"First, get a clear notion of what you desire to accomplish, and then in all probability you will succeed in doing it..." -Henry Maudslay-