I think you might be running into issues trying to forward non-http traffic through an http proxy. Proxies are a bit out of my area so consider this answer a best-effort from a non-expert.
If the UF is using https and operates strictly through the REST API then I would expect it to work with a web proxy. If the UF uses some other application protocol, or there is something weird about how the UF uses https, then an http proxy would balk at the request because it could not parse what the UF is sending. I would expect a well-behaved proxy would return an HTTP error code, probably something in the 400-500 error code range. That might show up in the UF logs.
I do not know about Apache but I believe nginx can act as a TCP proxy. That approach might work, but it's not something I've used or researched in depth. I'd talk to your local proxy administrator for some expert information.
If you have the option, I would suggest skipping the proxy and manage the UF manually.
You'll also need to have a solution to cover log forwarding from UF to your internal Splunk servers (which happens using a proprietary protocol). I would recommend having a conversation with your networking folks about what options you have to pass the traffic Splunk needs to your private network. A NAT would be one option.
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