Im only about 135 pounds.
Unless you have an extraordinarily low body fat %, and your height is in average proportion to your 135 lbs. weight, you might be in the category of riders that Ducati Performance is targeting with the lowering kit:
Ducati Performance Bike Lowering Kit (-25mm), Monster 937, 937 Plus I don’t know what the spring rates are for the fork and shock springs, but the first thing I noticed is that the kit replaces the stock progressive spring with a standard one, so the rate is at least constant through its travel. I think it would be reasonable to assume that the lowering kit would have lower spring rates as well as spring lengths for both the forks and the shock to compensate for the lighter weights of riders with shorter inseam measurements. Part number is 96280831AA; looks like it would need to be special ordered from DP through a Ducati dealer.
The other half of the equation that could explain your harsh ride experience is that the non-adjustable compression is also set up for a 175 lbs. rider. Short of revalving the fork, you might try increasing the fork oil air gap. Again, I don’t know what the stock air gap is, but that is fairly easy to measure, and then you could try reducing it by a few millimeters at a time with a Motion Pro or other fork oil height tool.
The good news in all this, if there is any, is that Öhlins USA says they will have stock on fully adjustable fork cartridges and a fully adjustable replacement shock for the M937 in November. They already have a range of 43mm fork springs and presumably will offer some rate choices for that shock. It’ll cost you $2k, so maybe save up and get those.