That trigger MIGHT be fixable, if it were completely disassembled/rebuilt (it might have a bent internal pivot, etc) - but I wouldn't bother, as there's much better choices available.
Keep in mind the any trigger for a Mauser 98 should fit your Mark-X with little or no fitting - if not the stock inletting.
Ergo, a Winchester Model 70 type, 3-position safety which replaces the bolt sleeve/cocking piece will give you the safety you would like - but they're expensive ($150 +/-).
Once a bolt sleeve safety is installed, an adjustable trigger w/o a safety can be installed/adjusted ($49).
If you DON'T install the 3-position safety, then an adjustable trigger with an integral side safety can be had from Midway or Brownell's ($60).