You can get super cheap VPSs and use them just as a reverse proxy (with access via VPN). I host 11 servers using one single-core VPS as a reverse proxy. All data resides on premises, in house. I pay 10/yr for VPS. It definitely does not defeat the purpose.
Check out low end box. I found coupons for racknerd. I have one VPS that’s $10/yr, another that’s $18/yr. I’ve had zero downtime in the 18 months I’ve used them. No complaints from me. YMMV of course.