I need to REDUCE the carrier's shipping costs

I sell a very heavy and bulky product that is not very expensive. I lose a lot of sales due to the psychological effect of customer's rejecting the relatively high shipping cost (i.e.  product cost $150 but shipping is an additional $90).  I've learned that I can increase the cost of my product to $200 and reduce the shipping cost to $45 and make more sales.
PROBLEM:  Squarespace's "markup" doesn't allow anything but an increase in the shipping cost, not a reduction.  
I don't want to keep screwing around with my product dimensions and weights trying to "chase" the desired reduction. It doesn't work anyway due to the screwy way the carriers have to calculate their cost.  I need a simple, behind-the-scenes "50%" reduction on the carrier's calculated rate.

Has anyone found a workaround or solution? 

I'd love to know if you found a workaround.