Starting demos desync

- [x] I have checked the known issues and searched Github to ensure this issue has not already been reported.
- [x] This is not a feature request, I know those belong on Discord/Github Discussions.

### Description of the bug:

When restarting lighthouse it causes the demos to desync.
### Can you reproduce? If so please list the steps:
- [ ] No, I cannot reproduce this bug
- [x] Yes, here are the steps to reproduce the bug:
1. Start Lighthouse.
2. Start any file.
3. When normal gameplay loads press the restart button on the lighthouse menu.
4. Wait until a demo loads. (May desync at different points and at different demos.)

### Expected behavior:

Doesn't desync when restarting lighthouse.
### Screenshots or videos:

### System Information:
- OS: Windows 11
- GFX Backend: DirectX
- Game Version: 1.1.0
- Rom Version: NTSC 1.0

### Additional Information:

Reproduce the issue by starting Lighthouse, launching any file, entering normal gameplay, pressing Restart in the Lighthouse menu, and waiting for a demo to load. Compare several demos and note when desynchronization occurs; done means restarting Lighthouse no longer causes demos to desync on the listed Windows 11, DirectX, NTSC 1.0 setup.

Written by the indexing model from the issue text.