Struggling with adolescent dog bitting

My dog is a 7 month old border collie Shepard mix. We adopted her 1 week ago, she spent a couple months at the shelter and was a stray/abandoned.

She bites a lot. Never aggressive, just playful. There are two main situations she bites during:

1. Softer bites while resting. especially if we try to pet her and she hasn’t had much activity for the day. These usually stop if we either hide our hands or if she is properly tired out. Not my main concern.
2. Harder bites while playing. These are the ones that scare me. My arms are covered in bruises and I’ve honestly been dreading playtime due to it.

We’ve tried (with no success) holding her mouth shut (which we’ve now learnt isn’t a good practice so we’ve stopped), redirecting with a toy, rewarding her when she goes for a toy, yelping when she bites and scolding her. stopping playtime and ignoring her when she bites has had medium success.

other than the bitting she is very well behaved, likes her crate, no accidents, minimal barking, doesn’t chew stuff up.

because of her breed i’m wondering if she is not getting enough activity. she consistently gets 1.5-2 hours of walks a day with usually 15-30 minutes of tug indoors and 15-30 minutes of more strenuous fetch outdoors. we’ve been inconsistent with training sessions due to busy schedules but she knows sit well and we’ve been practicing stay as well.

my question is, should we be following a more consistent exercise schedule. I’ve found that if we play too late in the day the bitting is worse (probably due to her being overtired). she usually wants to run around the yard after a walk so i’ll play fetch then but i’m wondering if she may be too tired after a walk to listen.

the other struggle is that playing is the most effective way to get out her energy yet we often have to cut it short due to bitting.

i know every dog is different but i’m really struggling here and wondering if anyone has any advice or suggestions for an exercise schedule.

TL;DR: 7 month old Shepard border collie mix bites a lot, interfering with play. looking for suggestions on stopping the biting during playtime as well as some guidance on an exercise schedule.