So, choosing the block rate of an alternate chain utilising the same hashing network, is tantamount to choosing it's difficulty ratio with the man BTC chain.
And I propose that this maybe "fix" its relative security, desirability and thus price relative to BTC. E.g. The alternate block chain could have a block rate of 1 per minute (faster confirms) but it's network difficulty would be 1/6th that of BTC and thus it would trade at approx. 1:6 ratio with BTC.
No. The price of bitcoin does not depend on difficulty but on demand and supply. Although security increases demand, demand is not directly proportional to security. If otherCoin were just like like bitcoin but with a monetary base of 300 M instead of 21 M (and a block per minute instead of each 10 minutes), they wouldn't trade at a 1:10. If otherCoin had different properties (rules) than bitcoin, the demand would be different too.