The first point is irrelevant. Yes it'd be great if we could always find players who no-one else knew about & who would only come to us, but that clearly isnt the case here. So yes, the other suitors do influence the price.
On your second point, Raya pretty much outperformed all those keepers this season, other than perhaps Leno, so yeah, I'd say he's worth more than them. Doubly so when you look at the profile of keeper we're looking for. The idea that he's comparable to Martinez is particularly daft, he was crap this season, in the league anyway. Pope was certainly great value, it's not often you get a keeper that good in a relegation fire sale. We should have moved on him, but we didn't because we kept faith with De Gea. We missed out. if there's another keeper on the market as good as him at that price, I'm up for that. But I'm not aware of any.
As for the Woodward jibe, I can hardly think of a less Woodward-like deal than David Raya. Giving David De Gea a long-term contract as the best paid keeper in the world immediately after his worst season, that was peak Woodward.