There have been products that you can apply to the inside. I don't recall by name, but I think they are related to the rust converters common to auto restoration type stuff. The real issue here is that you are unable to prep and clean the surface and there was likely lots of contamination in the fabrication of the frame simply from handling the tubes. This contamination was then cooked by welding/brazing for steel. For internal tube coatings, it is probably only mildly effective for the old highest end cromoly tubes like the Reynolds triple butted stuff. Protecting the center of that kind of tube is important because they are so thin.

In reality most steel bikes will fail with fatigue cracks around the bottom bracket. Those are usually fatal. Occasionally the seat stays will fail at the seat tube, or stays around the dropouts, but those are usually from latent manufacturing defects. Anything around the head tube is usually indicative of a crash or dropping of some sort, and the drive side chain stay and seat stay are very subjective to the types of damage as these are often damaged by a badly setup rear derailleur (not applicable here). This is how I asses all damaged frames at a glance and know if I should warranty something in a shop. I'm mostly from the post steel era in bike shops, but still know the basics. I'm also assuming that Mongoose was all steel.

If it was aluminum and you have cracks, that is game over without exception. Aluminum is a different set of issues entirely, but you are unlikely to ask about corrosion with aluminum.

Post some closeup pics of the damage some time and I'll tell you what I see. I used to have a structural steel welding cert, owned a body shop twice, and spent years as a Buyer for a chain of high end bike shops. I might be able to tell ya a thing or two if I see the issue.