Yes, welding or brazing a cross bar in that is long enough that it really cannot pull out of the opening should be plenty strong enough. If you had to , you probably could take the top tank off the radiator and do the repair. While the tank is off, it is pretty easy to really help the performance of the core by flushing out the flues while poking a "rod" down from the top.
Link to a thread where I did this on a D6 9U a while back. Have also done a 12E grader radiator. Both times it fixed the problem completely even though we were not able to clear all the flues, probably got over 3/4 of them if not more. All in all, pretty easy to do compared to removing the radiator. When we took the top tank off the grader, there was a double handful of rust flakes laying on the top of the core. Simplly scraping that off probably helped immensly, but a lot of the flues were plugged. The 9U wasn't nearly as bad. I had run some muriatic acid through it a few years ago, but couldn't get it to quit overheating while pulling a disk around. I think it might help the process of cleaning the flues if you ran some radiator flush through it before you take the tank off. Just to soften up some of the crud ahead of time.
http://www.acmoc.org/bb/showthread.php?17111-D6-9U-running-HOT-and-radiator-cleaning&highlight=Radiator
D2-5J's, D6-9U's, D318 and D333 power units, 12E-99E grader, 922B & 944A wheel loaders, D330C generator set, DW20 water tanker and a bunch of Jersey cows to take care of in my spare time😄