You can see what drew me to choosing this character as the donor of the Doctor's future DNA - his name. Doctor Peter Lord. Doctor. Lord. As in the Time Lord, the Doctor.
Sometimes I allow changes in historical dates - after all, we're dealing with Earth Prime-Time, not Earth Prime. But here we have an opportunity to suggest a reason why the Doctor and Ace would have been in 1937 - someone had tampered with the timeline. The difference in the dates for the death of Gershwin may have seemed a trifle to some, but it could also have a ripple effect leading to huge ramifications down the timeline.
Who to blame? Why not the Meddling Monk? It would have been the perfect opportunity to re-introduce him into the series and he would have been a wonderful antagonist to Sylvester McCoy's Doctor.
THE MEDDLING MONK
[A Casting Suggestion?]
It could be that location which also drew the Doctor and Ace back to 1937. There's a possibility that a Weeping Angel was in the area.....
If you'd like to see that Poirot episode "Sad Cypress", I've embedded it for you from YouTube: