you are almost right. I wouldn't call blinds as a late position.They are just blinds. They act last in 1st round of betting (preflop), and first in next round of betting (flop, turn, river) if they are still involved to a hand.
You write LP. The truth is late positions are cutoff and button. So I would use this system to write it correctly:
8 players EP MP MP MP LP LP SB BB
7 players MP MP MP LP LP SB BB
6 players EP MP LP LP SB BB
5 players MP LP LP SB BB
4 players LP LP SB BB
1st LP is cutoff
2nd LP is button.
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