TP-Link 8 Port Gigabit Switch | Easy Smart Managed | Plug & Play | Desktop/Wall-Mount | Sturdy Metal w/ Shielded Ports | Support QoS, Vlan, IGMP and LAG (TL-SG108E)

What you're doing sounds reasonable to me with the exception of why on earth would you want to move the service entrance when you're going to want the main modem and router in the house anyway? If it was me with that limited budget I'd probably hunt down some openwrt-supported routers for the garage to use as access points, run them into a switch then back to the house. Rip the casing off or modify it for air flow, and slap some extra heatsinks on the chips. I'd use a thermal camera to identify where they're getting hot and need extra attention. Amazon has this on sale, which does not have poe but does have vlan support for if you want to work on isolating your garage traffic at some point. https://www.amazon.com/dp/B00K4DS5KU