I have heaved-to in 40-kt wind. My boat (HR-39) is of similar displacement (10-T) to yours - with a bit larger sail area.
I assume your Tayana-37 is the cutter rig version. In any case, she is a "long" if not full keel configuration and my boat is fin-keeled. My guess is that your full keel might behave, if anything, better than a fin while hove-to.
My boat is sloop rigged, but carries a stowable inner-forestay for use with a staysail. We heaved to with very good results in 40-knots with 4-6-foot steep chop. The mainsail was reefed to a deep #2 reef and the staysail (~200 sq ft) was rigged. The working jib was completely furled.
I eased both the main and the staysail sheets as though I were on a close reach then put the bow through the wind - leaving the staysail backwinded. I tightened the wheel lock nut with a bit of weather helm correction set in the rudder.
I was very pleased to see that the boat tracked nicely - forereaching at about 2-kt into the wind with no tendency at all to roll off to windward or leeward. Unremarkable results I suppose, but still a very nice surprise for a fin keel, semi-skeg rudder configuration boat. I think I went below for a snack of Stugeron.
My guess is that your Tayana will do quite well hove to.