If yields are not a concern, I see a way for you to reduce the preparation of your gamma lactam by a few steps starting with nitromethane and methyl acrylate. The reduction of the 4-nitro-butyric acid methyl ester intermediate using appropriate conditions might even proceed with concomitant lactam formation.
Nitromethane is produced commercially from propane or chloroacetic acid. How is chloroacetic acid prepared? Interestingly enough, acetic acid can be synthesized from methanol in one step. Look into this to see how many steps you can shave off your synthesis.
The most important component in any organic synthesis is to have 1-2 backup plans. Regardless of what backup plan you use, I believe your professor will be impressed that you considered it.
Good luck!