If you change how you process your film, and you shot a normal contrast scene, your final negative will come out with lower contrast, and the only way you can counter that is to use a higher contrast paper.
If you develop 'normal' with an overexposed negative, you will retain the full negative contrast, which enables you to print on a normal contrast paper. The only thing you have to do is to open up your enlarger lens, use a stronger light source, or simply just expose the paper longer.
This gives you MORE flexibility at printing time, because you can still default to a higher grade paper if you need it for artistic reasons. But if you have already used that higher contrast to compensate for a low contrast negative, well you're out of options. Some of it can be remedied by using a high contrast print developer, like Dektol, of course.
Anyway, if it were me, I would shoot another roll/sheet of HP5+ in similar conditions with the same gross overexposure, and then test my way to the best likely outcome before I processed the very important ones.