Number 1 actually helps teams get more value from the offer sheet than they otherwise would because it artificially makes the aav higher for the purposes of compensation. Yes it's a bit of a poison pill but this shouldn't be something that happens on a consistent basis.
For Number 2, you could put a couple of modifiers. For example, the "not your own pick" can only be for picks in rounds 2 (or 3) and up.
Along with that, for the scenarios whereby teams would be acquiring the picks to give them the lower ones, you could make it so that if there are multiple, the team who's player was offer sheeted and are therefore getting the picks could choose which ones they want.
Ultimately though a team wouldn't be able to go out and acquire a pick after the offer sheet was made and signed to get "lower value" picks because it would be based on the picks they have at the time of the offer sheet.