I only found out about these guys recently, but these guys have been running an amazing Series of fanmade Doctor who since at least 2013, and they just aired their own special for the 60th anniversary!
Entire official youtube channel:
Playlists of series:
Series 1 on Youtube (HD Official Remaster from 2019)
Original Series 1 & 2 on the Internet Archive (2013)*
Series 3 on Youtube (2015)
Series 4 on Youtube (2016)
Series 5 on Youtube (2022)
*= The original Series 1 and Series 2 were removed from their account to be completely re-filmed to be up to their current standards, HD Series 1 premiered in 2019, and I have no idea when HD Series 2 will go up. Thankfully I found someone who'd archived the originals, so I can finally watch the whole series in order!
If you're already all caught up on their series, you can watch their amazing Part One of their 60th Anniversary Special here!
I think it would mean a lot to Kate Stewart to meet the Doctor who ultimately started her father's UNIT journey. Because of Timey Wimey stuff she can't tell him who she is of course, but she can still show some thanks.
Bonus:
I like to imagine since Donna works for UNIT now, she likes to ask Kate along for lunch occasionally. And I also think 14 wouldn't hear the END of it once she finds out about Jamie.