Probably no wireless mesh system without dedicated backhaul will be able to do that for you.  The system has to share the two bands that the Beacon has with the backhaul connection between it and main Eero, as well as your client devices.  Systems like Orbi will be able to do what you want in terms of speed, but my experience with both Netgear Orbi and Zyxel Multi X (both have dedicated backhaul bands) was terrible - really unstable and I had issues with satellites and/or clients dropping regularly, sometimes every day.  You could hardwire  a couple of the new Eeros to your system and will get full speeds everywhere if you do that.

I'd try moving the beacons around. Just because one is right on top of the other, one floor up doesn't mean there will be good connectivity. Maybe there is a bunch of electrical wire between floors or pipes or who knows what. I got lucky in my setup. I use ethernet to connect two of my Eero Pros and the third is one floor above one of those and it is working well.

Wireless nodes placed directly above each other on adjacent floors is a bad idea per the lead designer. Offset them a bit diagonally as there's a hole in the radio's wifi radiation pattern directly above and below the eero casework if I recall correctly. 

**I reported my own post as it was flagged pending review - not sure why**