Intense gas pedal vibrations at high rpm

Intense gas pedal vibrations at high rpm under load in my 2003 Mitsubishi
eclipse spyder gs 2.4L

I have been trying to fix my car with my father's help for the past month or
so. Usually I go to a mechanic but the problems were with the engine and all
local mechanics were charging way too much.

A little history:

My car lost its timing belt. I got the cat used so I did not know the belt was
due. Upon opening the rocker cover, it was clear that all the valves were up
when it blew (or at least we think it was clear. No damage was visible but
we're by no means mechanics) so we decided to try replacing the belts and
seeing what happened. Now my father did moat of the disassembling and I
helped putting the belts on. The car fires up! So excited! I tried driving a little
(just running some small errands) and realised all was not well. I noticed
jerking from shifting gears and vibrating at high rpm. "crap maybe a valve is
bent". So I did some research and found it could be that I need an oil
change, need to put a proper gasket on the rocker head, or need a new
motor Mount. Okay fine did all those (one Mount was broke) and it fixed the
jerk! Go for a test drive and it drives normal until you get ~1000rpm from
redline. At this Point the gas pedal vibrates violently.

The symptoms:

Car drives fine until ~1000 rpm from redline. At this point the gas pedal
vibrates violently, but the car will still increase rpm. There is no shaking at
lower rpm. Speed does not effect the shaking, only rpm. Happens in first and
second gear, I cannot test third and fourth as I don't drive that fast on public
roads. Idle seems fine. Doesn't happen out of gear.

What I've come up with:

By researching and talking to friends I've found This couldn't be a wheel
alignment, or it would happen at all speeds and get worse as I go faster.
There was a guy who had a Ford gt with similar symptoms and it was in
need of a transmission alignment. I have no idea if this is a thing but I hope
isn't the problem. I don't see how the transmission could have been
misaligned Anyway. One of the timing gears is off by one tooth. This could
be the problem but I don't know if it would cause shaking at high rpm and we
double and triple checked it. I wouldn't love pulling it apart again to check
again but I may have to. A valve could still be bent I suppose but again I
don't know if it would do this. The forum about the Ford gt also mentioned
the engine could be getting starved of gas, but I don't see why it would be
now when it was fine before. Unless of course the timing is off by a tooth and
it's spitting gas at slightly the wrong time.

I'm pretty deep in this project now and really just want to drive my car. My
father is fed up and wants me to just drive it but I don't feel safe. I appreciate
any help/input/ideas anyone could provide. Thank you.