I want to control these devices

1. Epson PowerLite Home Cinema 3100
2. Vinciper 3-port HDMI switch/audio-extractor [Link: amazon.com]
3. Musical Fidelity MS3i integrated amp
4. Sony Blu-Ray Player BPD-S3500 (unsure if that's the correct model)

The remotes are shown in this photo [Link: photos.app.goo.gl]

I highlighted in green the buttons I use on remotes for 1, 2 and 3. On remote for 4 I don't use the buttons highlighted red.

I'd like to spend under $50.

What do you suggest?