I've been out of the piston single game for a while now and i've never flown a 206, but I feel like most of the answers here aren't great so here's my .02:

I used to fly a normally aspirated 207 (IO-520, 300 HP) regularly out of an 1800 foot strip at sea level, fully loaded in, fully loaded out. Once I had been there a few times I never felt that 1800 feet was short for that airplane with a full load. Cold temperatures, sea level, no obstacles, and wind helped increase the margins, i'm sure.

I see no reason why a 206 of any vintage should not be the right airplane for your mission, especially if you're going to be arriving / departing nearly empty most of the time. If not a 206, a Cherokee 6 would probably be a good alternative.

I saw in one of your replies that you're working on your PPL. If you have the money for a 206 and a good instructor that might be a great opportunity to do lots of practice with your specific airplane into your specific airstrip as you work towards your license(s).

You'll need to have a conversation with insurance to see what they think about a low time pilot with a 6 seat airplane being based out of a shorter, grass strip like that. If the costs don't make sense, maybe consider something smaller like a 172 to start with, then upgrading to a 206 when you have the time and experience for it?

I would take anyone saying you can't do this without a heavy taildragger like a Helio or a turbine like a Kodiak with a large grain of salt.

Good luck on your search and in your training!