GTM hands out private IP addresses, need it to hand out public/translated IPs

If I understand your description then the addresses are backwards. The address field in GTM is the public IP and the translation field is the private IP. GTM resolves using the address field and the monitors also test the IP in the address field so in your case GTM would not be able to check port 8080 on the pub IP.

 

I have not tested this (pretty sure it will work) but you might be able to work around this by creating two servers/virtual servers, one for the public IP and the other for private. Then in the public virtual server properties set virtual server dependency so it depends on the private addr virtual server. Assign you monitors so that if the private VS is unavailable then the public VS will be marked down also.