I wanted to follow up here, it's been a very long troubleshooting session and I think I finally found the answer.

Programs which stop the drive from ticking didn't work and besides if you plan to never use a floppy drive it's pointless.

I finally came to the conclusion that this may not be the computer itself.

I purchased a VGA LCD monitor which supports 15khz modes, and surprise! No screen jumping.  I also tried a VGA CRT which did not support 15khz, and it also had no screen jumping.

Lastly, I tried a scan doubler on the VGA CRT and no loss of sync.

I started going thru the main board with help from grok, because the schematics which are available on zimmers.net do not actually match my 1084S-P monitor.

In fact the schematic for the PCB is a different CM8833 based monitor which looks similar to the Daewoo monitors.  It took many many rounds of correcting AI to finally get the correct schematic and despite the frustration I confess I am grateful for AI's help.

I finally managed to determine which capacitors may be failing and found one which had no signs of leaking but was completely dried up and tested as open, then I found another 250V polyester film capacitor which tests good but has a burn mark on the side of it. 

I replaced the first capacitor and this greatly reduced the flicker and jumping of the screen, but caused the screen to shrink vertically beyond the vertical size control is able to correct. Apparently this is a side effect of the now working capacitor, but also a remaining bad capacitor further along which just so happens to be the one with the burn mark on it.

I'm waiting for that cap in the mail but I can clearly see I am on the right track.  The most interesting thing about this issue is that it is the worst when the amiga is playing music.  Apparently it's just noise in the sync signal which the 1084S is no longer able to filter because of the bad capacitors.

I will provide more details once I confirm the repair.  Even though Grok was wrong about 80% of the time, it did finally help me find the correct schematic and explain the role of the capacitors I discovered which were bad, confirming they did have an effect on vertical picture size.   I saved the entire grok conversation which is sort of funny if anyone is interested in just how many times AI got it wrong.

One more week to WOC 2025 Toronto

It would help if you stated what country you're in

No, only Windows, Linux, macOS.

But your answer brings me back to the earlier post about emulation. Just get WinUAE or AmigaForever, emulate a AmigaOS 1.3 system and use AmigaBASIC on it. Otherwise if you wanna code on Windows but want the programs compiled for m68k AmigaOS you would need a cross-compiler, and I'm afraid such thing is not available for AmigaBASIC.

So if you just look for any Basic usable on Windows and compatible wih QuickBASIC, then try QB64-PE (https://www.qb64phoenix.com/).