Sea Service on Non-Self Propelled MODU

I hold a third mate unlimited license, working temporarily on a non-self propelled MODU. The rig is currently in the shipyard, moored alongside the pier while the yard is working on it. I am assigned to the rig temporarily to assist with getting it up to snuff for the USCG certificate of compliance to work off the outer continental shelf of the US, as it is foreign flagged. I work 12 hour days.

My question is whether or not my time onboard can count as sea time. As this is not a dynamically positioned unit, and being that we are not underway, it is unclear after reading 46 CFR 10.211© if this qualifies for sea service.

Furthermore, I rode on a heavy-lift vessel that carried this rig from one port to another, a 9 week voyage. I rode the HLV as a representative for the company which owns the rig (the company I work for), not as a third mate, since the HLV was a contract vessel and had its own crew. I was there to maintain contact with the company about the voyage/weather routing, etc. I seriously doubt I can get any sea time there, as I was not sailing in the capacity of third mate, but I figured it is worth asking.

Anyone? Thanks in advance for your help.