1. What has 'could not read' have to do with it? In Cymraeg, the two names are pronounced very differently(especially in the North).
There was noone using the name. Until the Breton name was introduced. So, the only way to encounter the name would have been to read about it. Which they couldn't do.
The pronounciation you are referring to is modern. Medieval pronounciation was more variable (see info on ah/eh below).
2. "if they existed, they would have died at least 500 years before his time" Don't understand your point? Why is there a 500 year gap?
Alun - river name. First recorded when? Never actually recorded as a personal name, so if it was a personal name, we must assume it was rare, and already out of use before 700ish. Alan - given name. Not recorded in Wales until at least the 11th/12th century.
So the name would have to survive as a given name, despite being unrecorded as such anywhere, and then coincidentally reappear at the same time as the Breton name appeared? Unlikely. Fails the 'Occam's Razor' test.
4. "and your father, and his father". It's grandfather to grand son.
I thought you said it was your father's father's name as well. I was just listing the family members you listed.
5. "Unless your family tradition of Aluns goes back a thousand years (unlikely)". So if I was able to show you my family (Llywarch) tree back to the year 1004, and show you all the Alun-s, you might belive me?
If you could show me an Alun definitely born in Wales between 900 and 1000, with no possible Breton connections, and then an Alun at least every 5 generations (say), I would consider the possibility that Alun as a name survived in Wales, and does not solely represent a form of Alan arising from the medieval habit of confusing ah/eh sounds (i.e. in Medieval England and Wales, Alice and Ellis are interchangeable when written, and Alan is also found as Allen/Allyn (thus the surnames).
It's not a matter for 'belief', it's a matter for knowledge, and common sense conclusions.
6. "Welsh and Brittonic are two similar languages, but they are not interchangeable" Sorry, might have to explain this one to me also. Being Cymraeg first language, I am able to read and understand 80% of all Brythoneg litrature I have read.
There is no Brittonic literature. If you're thinking of the Mabinogion, that's not Brythoneg, that's Middle Welsh. There is also a small amount of Early Welsh - actually, one poem in a margin.