I don't have the budget to throw at a telescope at the moment, so what could I expect from 200mm or 300mm lens on 35mm?
I have a Nikon F100 that I could use and and Pentax Spotmatic with plenty of Takumar lens.
Would those x2 teleconverters work with my 300mm lens for this application? I never used them with astrophotography before.
Apologies if I'm wrong, but judging from your first question, you should probably familiarize yourself with some general knowledge about astrophotography. Any lens can be used for astrophotography. Telescopes are, in general, just long(er) telephoto lenses. You can use some astronomy software such as Stellarium (with the "oculars" plugin) to see what kind of FOV you get with your camera + lens combination. You can also use the online Astronomy Tools FOV calculator in imaging mode and see how the Messier objects are framed. I would not suggest using teleconverters, they are usually not good enough for astrophotography and increase the f-number so you will need much longer exposures.
To stay on the topic of film astrophotography, you must be aware that exposure times on film are much longer than for digital. To get sharp stars and reduce vignetting on camera lenses you need to stiop down the lens by preferably two stops. This again requires increasing exposure time. With increased exposure times your tracking accuracy becomes critical. The longer the focal length, you polar alignment and tracking needs to be even more precise. As mentioned, in film photography we need long exposures which means you won't get sharp stars if you don't correct for the mounts periodic error. There's no way you can get pinpoint stars with a 200-300 mm lens in 10-20 minute exposures on a tracking mount without guiding corrections and precise polar alignment.
I'm attaching my "beautiful" long exposure photo of the Lagoon Nebula and it's neighbours, taken with a 180 mm lens on Kodak E200 diapositive. But when you take a look at 100% crop...it's not usable. So, before jumping into long exposure film astrophotography with telephoto lenses, I would suggest you try some tracking shots with a normal 50 mm fixed focal length lens. The slowest are usually f/1.8 which you can stop down to f/4 and get stars that are sharp enough at the edges and also reduce exposure times to 5-10 minutes. At 50 mm the periodic error is not that visible and you will get more keeper photos. I would also suggest you try this first with a digital camera and a 50 mm lens, so you can immediately see if there are any errors. This way you can correct them on the spot, rather than wait for the film to be finished and developed. You should use the digital technology to speed thing up and help yoo immediately take good photos on film. There's absolutely no need to do it like it's the '80s, it will most likely result in frustration and abandoning film astrophotography.