The problem is not with the Hebrew. Its with the English.
Look at the English in Yeshayahu 53:8. “for the transgression of my people to whom the stroke was due”. It sounds like a Christian translated that. If you look at the Hebrew you will see that it should be something like “from the transgression of my people they were plagued”.
Look at Yirmiyahu 31:32 “I will put My law in their inward parts, and in their heart will I write it”. Again, this translation sounds like it came straight out of a Christian’s head. From the Hebrew it should say “I put My Law in their midst and in their hearts I will write it”. The meforshim there explain that ???? is “??? ????? ????” and really it should be read as future. But that is exegesis not literal translation.
My problem is that any Christian can come along and say “look even your Jewish Bible agrees with us”, because these translations just aren’t that great. I know that the Chabad site uses the same translation for Yirmiyahu, but at least over there we can argue that they are basing it on Jewish commentaries not strict translation. Mechon-Mamre’s thing though is “Bible and Mishnah Torah for all- Jews and Gentiles”. If they expect goyim to reference their material, then they should be more careful in their translations.
You are right that JPS isn’t technically conservative- its non-denominational. But calling yourself a duck won’t make you fly. Practically it seems to be run by Reform and Conservative.