Will a Supercharger increase my towing performance? Also, towing an Airstream Bambi.

I tow a 18' travel trailer with my 2000 3.4 manual Tacoma. I'm supercharged with 220k miles on the truck. Currently running 255/85r16 on stock 4.10 gears. The supercharger helps with gear holding power for sure, I'm sure it would allow you to easily go 75 mph, I don't like going faster then 65 though. I mainly notice the extra power towing in the mountains, easily holding speeds that are safe for travel while still passing Subarus and VWs and other mid 90s cars. I also have a 2004 4runner with the 1GR engine, it is on par with a 3.4 supercharged, there is no gains/losses when towing. I wouldn't sell what I had to get a 2nd gen Tacoma for towing, just not worth the minimal gain. I also wouldn't get a full sized truck because 95% of the time I'm not towing so why take the fuel mileage/cost hit.

Dealership labor times should be in the 4 hour range for a 3.4 supercharger as specified by TRD. It is really as simple as remove manifold and belts, install new parts. It takes about an hour for an experienced technician. TRD no longer sells the supercharger so good luck finding one but they did cost around $3k new from a dealer a couple months ago. Now you are stuck buying NOS for an inflated cost or used. A quick search online nets no results for new or used for sale.