Dear Querist,
I re-visited the issue, specially after noting that supplier is also located in state of UP from your post at Sr. No. 5.
In my view, under plain reading of current position of law as well as the way GST portal operates, there is no option for the said Co. but get itself registered in state of UP and pay CGST & SGST under RCM therefrom.
In other words, even if said Co. has neither a 'fixed establishment' in UP nor it is 'casual taxable person' for UP (though I doubt this very much, due to reasons explained in earlier posts & hence, I didn't give deeper thought for other complexities), still, it needs to get itself registered in state of UP on account of subject transaction due to requirements of Section 24 (3) read with Section 25.
Only way to avoid this is to argue that Co. is not registered in UPGST (state gst law of UP) and thereby, subject services are not received by a registered person so far as UPGST act is concerned. But, fact remains that said Co. is actually registered for CGST and IGST and hence, such argument seems quite risky.
Now, considering this compulsion of separate registration anyway, it would be necessary to re-check if said Co. has a 'fixed establishment' in UP or not. If former position is accepted, many other potential risks can be potentially avoided.
P.S. Taking any arguments to claim non-liability itself may invite deeper scrutiny about Co's operation (due to reasons explained in my earlier posts).
Thanks for raising such an interesting & challenging query! And I am sure my ex-views here are not end of it for me too.
I would urge to other professional colleagues on this forum to put their views.
These are ex facie views of mine and the same should not be construed as professional advice / suggestion.