Amp question with size constraints

An AGD Tempo power Amp and Alto preamp will solve your problem and sound MUCH better than your rega (and should since they are 10x the price).  They will easily fit on your shelf and will only require a .5M set of XLRs to connect.  The phono stage in the Alto is excellent.  The power amp (tempo) is a good match for Fyne and tonally sounds like a much more refined Rega.  If you want a DAC included, then the Andante becomes the first choice as it has all the functionality of the Tempo plus a superb R2R DAC and Player/Renderer on-board.  

Either is a rig worthy of your turntable and speakers.  

Full disclosure, I am an AGD dealer but you will note it has been mentioned above by several people and for good reason.  Also note that not all GaN (Gallium Nitrate) amps sound the same.  If your preference is Rega and you like a warmer, more romantic sound, AGD is THE choice.  

Audio Alchemy made some small (and shallow) kit that sounds quite good and can be found very inexpensively on the used market. His designs can also be found under the Elac name. I have owned the stereo amp and still have his DDP-1 (dac/pre) + PS 5 outboard PS; he also made a very small phono pre

You won't be disappointed with either the price or performnce

Mono Blocks would fit more readily, then do you have an existing preamp, existing phono stage, remote control?

Thanks for the support @shkong78. If anybody has questions, feel free to reach out.