First and rev are low gear ratio. The most "load" on clutch and etc. Don't know what trans you have yet. Four speed with granny low?
1. If four speed, you don't use first to "accerlerate". You ALWAYS start out in second. Never in 1st (compound low) except to crawl or pull a stump. 1-5 MPH range.
2. If four speed, it is cantilever mounted off of bell housing. Assume the crossmember you speak of is for a truck bell housing side pad mounting. Pretty easy to inspect that crossmember/rubber pads for loose. You can call those bell housing mounts "rear engine mounts" or other names.
3. If you agree with 1 and 2, and still have shutter, it can be a bad clutch repacement job, bad ujoint replacement job. Possible just needs adjustment.
4. Maybe you have a column shift?...or a non original trans.
We do need a little more info as to exact equipment. And many pics for us to pick up what may be wrong from our house.