Question on wife's Hamilton

[samson66]

I purchased a Hamilton Jazzmaster 34mm for my wife almost exactly 4 years ago for our anniversary. Looks like the picture below.

She still loves the watch and wears it all the time. Perfect size for her.

Unfortunately about a year ago it started running fast, like >1 min per day fast. I took it to a local watch guy thinking it had maybe been magnetized. He took a look at and said the oils have started drying out and it needs an overhaul.

Quoted me around $350 to do it. The watch brand new was ~$500 so I said no. My question is #1 should I get it serviced or just scrap it and either live with it or buy a replacement? And #2 could anyone recommend an alternative for service that would cost me less? I am more than willing to ship it out for a couple weeks to get it done. Not sure whether to ship to Hamilton directly or if anyone can recommend another source?

Thanks in advance for any replies