First off, a few words as a fellow consultant. You probably are well aware of what I'm about to say, but, nonetheless... Past a certain level of cost-cutting/denial, I would put your foot down on a minimum level of product/service here. The client simultaneously complaining about a sub-par experience while denying your suggestions to properly remediate doesn't do anything other than bankrupt the both of you, slowly but surely. That said, I'm sure there must be enough upsides to retaining them as a client, and good on you for trying to work within the confines of their needs.
Moving onto gear. As you're probably well aware, you need to progress to a business-class stack. Lowest hanging fruit is that Google product, in trade for a solid firewall and wireless.
Firewall - While an EdgeRouter, Mikrotik, Cisco RV or similar solution would likely handle the traffic load and core services, they may lack certain AAA and/or UTM/NGFW functionality required, either now or perhaps within the life-cycle of the purchase. If you sense that might be the case, then you might be better off taking a look at pfSense, OPNSense or Untangle on an x86 box, or even an entry-level Fortinet or Sophos (you can forgo the extra licenses and just buy the hardware to start; all core services will still function).
Switching - Depending on the robustness and port count of the managed switch you already have, you may be able to just re-purpose that as your core for the time being. If not, replace with as few switches as needed to keep the LAN as flat as possible. Regarding Layer 3, unless you're locally routing a ton of data and/or control plane traffic, you can likely just leave it on the firewall, especially with enough x86 CPU and Intel I210 ports or better (for enough queues per port). It may not be a network engineer's wet dream, but given the other constraints here, that extra spend could likely be invested with greater effect elsewhere (firewall and/or wifi).
Wireless - Ideally, a single ecosystem (UniFi, Cisco WAP/CBW, etc.). Even TP-Link Omada would suffice if you have to; EAP225v3's are $60 each and the controller can be run for free on one of the servers, or the OC200 appliance is only ~$95.
Roll any appropriate combination of the above, and they ought to be in a
lot better shape than they're in right now. Minimum investment would be $350-400 total. If the client can't at least scrape that together, I'm not sure I'd want them working on my teeth, or anyone else's for that matter.
