I have 118 authentic JM exemplars in my files and only 13 of them are signed "Jim Morrison". All the rest are signed "JMorrison". There is only a few that are signed "James Morrison" or "James D. Morrison". A check signed JMorrison in my opinion goes for about $5k and the much rarer Jim Morrison check is about $6k to $6.5k in my opinion. Jack...
Your best bet to find one at that level will be in an upcoming auction.
If you are talking "auction prices" you're obviously not factoring in buyer's premium which can range from 22.5% to 30%. So factoring that in, you will never get one for under $5k.
Wow...the second one is KILLER!