In-universe reason for Peter Purves having two distinct parts in "The Chase"

Question

This question asked about actors who appeared in Doctor Who as various characters and then went on to play the Doctor. This question is about the First Doctor story The Chase. In this story, Peter Purves played two characters – Morton Dill (in the episode where they land on the Empire State Building) and Steven Taylor (the final episode on Mechanus, where he becomes a companion). Is there are in-universe reason for this? Was Morton Dill supposed to be an ancestor of Steven Taylor? Out of universe, was this cheapness, or perhaps someone didn't turn up?

Edit: Coincidentally I am just reading "Who's There? The Life and Career of William Hartnell" by Jessica Carney. On page 167 she writes "One day Bill [William Hartnell] and Maureen O'Brien [Vicki] hatched a plan. They decided they liked Peter Purves when he did a one-off character role in an early episode of a Dalek story, 'The Chase'; so they went to the producer and suggested him for the role of Stephen Taylor ....."

Answer 1

It appears that he was cast in that serial as a recurring character (the American hillbilly, Morton Dill) and the producers liked him so much that they cast as a new recurring player, Steven Taylor, who made his appearance later in the same serial, and then carried on into the next series.

Note that he grew a stubbly beard specifically so that audiences wouldn't get the two characters confused, suggesting that there was no in-universe connection.

Q: You played two characters in the same story – how did that come about?

PP: Because I successfully played Morton Dill, the American Hillbilly, I was asked to join the series permanently. The new character, Steven, appeared in episode six of The Chase. I grew the beginnings of a beard as a disguise between times.

_{^{Peter Purves: Taylor Made}}

Answer 2

Peter Purves was a young actor at the time, just 26 at the time, and beginning to build his career. He auditioned to play one of the Menoptra in The Web Planet, and did not get the role, but according to this interview

the director, Richard Martin,... very kindly told me that with the work I had been doing previously it wasn't worth me playing one of the non-speaking roles. However, he told me that if ever he was casting proper acting parts, he would think of me.

A few months later, Richard Martin indeed cast Purves as Mervyn Dill in The Chase. Purves recalls:

I was thrilled to be playing the part, but even more thrilled when I was asked to go with the Producer, Verity Lambert, for a drink at Studio 3, the pub opposite the Riverside Studios. I was dumbfounded when she asked me if I would be interested in joining the cast on a regular basis. Naturally I said 'Yes' and Steven Taylor made his debut appearance three weeks later.

So, as he remarked in another interview

in effect Morton Dill was my audition for the part of Steven Taylor.

The two characters he played seem to be completely unrelated, so there is no in-universe reason for the casting. It just seems to be that he impressed the producers sufficiently for them to offer him a permanent role.