When using a puller like Mikes’ it’s best to put a spacer between the parts being pulled and the bar so the centre screw or bolt can be done up tight. Effectively becomes a single solid unit vastly reducing the chance of thread stripping.
Way back young and hairy Clive stripped the thread on the centre bolt doing a similar job, fortunately not the extractor thread on the part being removed. Was advised to make things solid with a spacer and it all came out quite easily. As I recall it with less torque on the pulling bolts too. I presume with it all locked up solid the mechanical efficiency at actually pulling is much greater. Or something.
Probably unwise to use a high tensile bolt in the middle. Nice fitting ordinary bolt, something better than the rattle around big box store cheap ones, seems wise. If everything does go whaooie shape a HT bolt could well strip the thread in the part being removed. Which makes the problem ten times worse. An ordinary bolt stripping leaving the other thread intact is much less of an issue.
If need be and you have the facilities make your one with a top limit size thread for best grip. Something I’ve done in the past when I really didn’t like the potential fall out if things didn’t work.
Clive