It does sound like your fan clutch is not engaged as it should be and may be the root cause of your higher temps.
Ugh. This is a real problem nowadays. You can try one of the "thin" aftermarket clutches, along with a shorter center bolt (search the forum for details). Try to pick a recognizable brand and hope for the best. Another option would be to tweak the OE Sachs clutch bimetal spring with the Stu Ritter modification, which should get the clutch engaging at a lower temp. Be
really careful if you attempt this.
You can convert to an electric fan, but this is not easy and not cheap to do properly. It should be a factory fan from a mid-2000's MB and use a PWM controller. This is the best solution IMO but it's a LOT of work, and also requires upgrading to a 143A-150A alternator.
Yes - you must have the special tool to hold the pulley. Or you have to fabricate something to hold the pulley without damaging it. Also make sure the 8mm hex tool is FULLY seated into the bolt, and the bolt hole head is in good condition. If you strip out the socket head you'll be in a world of hurt. Once the bolt is free, if you re-install the OE clutch, don't over-tighten the bolt (a tiny bit of anti-seize on the threads won't hurt either). Don't discard either the OE clutch, or the original long bolt (also NLA).