Faketak lol, love it.
I’m not assuming anything though, PLA glass transition is around 60-65c and already gets very soft and bendy well before that… putting the bed at 70 is going to make the PLA extremely soft even after losses through the bed which will generally only exacerbate any warping issues when already present. I myself currently print on a tool plate aluminium bed, magnetic plate, spring steel and printbite+ so I’m well aware of the thermal losses involved.
From past experience while most works great at a nominal 60c, when I’ve had the occasional troublesome PLA brand lifting I’ve tried going hotter and had it end up worse… dropping down to 45-50 (and upping the first layer extrusion temp) solved it almost every time. It's pretty counterintuitive and indeed the opposite of what you would do for many other materials, but remember one of the big selling points of PLA over ABS back when it first started gaining popularity was how it can be printed without even needing a heated bed...
It’s just a suggestion for something to try from my own experience over many, many years of printing countless materials and brands... Given he’s already tried the bed at 70 and still had it lifting off the bed I would suggest trying going the other way too (and trying the other suggestions).
Ultimately I never particularly loved buildtak, I think there are much better surfaces out there. That said PLA should be able to be printed without issues.
edit - can you take a picture of the first layer so we can see how it’s laying?