Junkyard Bluebox

Culloden was an extremely one sided battle (1500+ Jacobite deaths to 50 British deaths), and after it was over the British didn't stop killing Jacobites and Highlanders, nor did they stop making their lives hell.

Jamie is so so brave he would not have gone down without a fight, but the only reason he got out of being sold into slavery in the first place was because of The Doctor. I won't get into how Jacobites/Jacobite supporters were treated both during and after the movements/the battle of Culloden, but it was extremely brutally and inhumanely.

If he did survive Culloden and it's aftermath, the Highland clearances just a few years later wouldn't have been much better. Highlander's homes were burned (sometimes with people still inside), and they were starved and forced to move from their homes, 70,000-150,000 people were forced to relocate, and many of them died from starvation and other complications. If Jamie is still alive by this point I doubt he's having a very nice time.

After Culloden, there was a ban on Highlanders playing bagpipes and wearing tartan, so he could no longer wear a kilt or be a piper :(

(People in the British military could still play the bagpipes, but I doubt Jamie would have been keen on that.)

old man Jamie is very cute in tales of the tardis but if Doctor Who was a touch more realistic I don't think he'd grow up to have a life this happy (or have grown up at all).

all this to say my headcannon is that Jamie died/was killed at most a few days after being memory wiped and sent back