Car Registration Woes

Need help here because not sure what I can do.

Timeline:

Early 2024 - I get a car from the dealership in GA and start financing it

Summer 2024 - I get a new job that moves me to TX. The job pays for me to stay in a hotel, so I don't really have an address

Early 2025 - I have an apartment in mind and want to move there in the summer. I get texas car insurance and register my car in Texas using my job as the address. The office says just make sure I change the address once I move in the summer and get a TX DL

Summer 2025 - my job moves me to LA -_- But in a position that comes with a lot of travel. I'm in the state enough time to get an apartment and then I'm gone weeks at a time, only really being home for like a few days.

Early 2026 - My TX registration is gonna expire soon and I never got a TX DL so I can't renew. I go to the OMV and they say I need LA car insurance. Which ofc, silly me for forgetting to change that. I leave for work and when I get back I go up to the OMV with my LA car insurance but the OMV said they need my original title from the lien holder.

So for the past few months I've been trying to get this original title. Called my lien holder asking for, had the omv fax them the form requesting it but everytime I go to the omv they say they haven't received it.

Present day, still haven't been able to get my registration. And my job said I could move back to GA. So now I'm going to move in a month which makes me not want to register my car in LA. But I don't want to drive it back to GA with expired registration. I could get it shipped but that's so expensive. I feel like temporary tag would be the cheaper option. However, LA doesn't do temp tag unless you're a dealership.

Just looking for some ideas