Heuer Autavia GMT 2446C repair estimate

I inherited this 2436C two years ago when my father passed. I finally was able to have someone look at it. They said basically it needs a full cleaning, the past oil has turned to dust. New mainspring, timing and Chrono adjustments. It is an heirloom so I don’t want any buffing or polish, just service and replace needed parts. Was quoted $1250 for the job. Does this sound reasonable?

Here was a video I made before it stopped working.

A couple pictures as well.

I'm currently looking for a watchmaker to service a similar GMT, if you went ahead with this, could you let me know who you ended up doing the work?
Thank you...

Ted