My own experience may not be yours, but it might help. I had my biggest problem with tongue bite with flavored tobacco, aromatics. I had one holiday blend flavored with cinnamon and spice that burnt like crazy. When I went to entirely non-aromatic, that helped. Later, I found I could smoke tobacco-forward aromatics with light flavoring, but leave that for later, I'd suggest. A glass of water will coat your mouth and reduce bite. Slow way down, and sip don't puff, lengthen your cadence.
I don't think timing a bowl will help. So much depends on how you smoke, and if you are indoors or outdoors, and especially on the cut and blend, and so on. Slow down.
Also, you can smoke a partial bowl, or smoke a full bowl intermittently, with breaks of an hour or a day, to see if that helps. You could try a filtered pipe, if you have one. You can always leave the filter out later. You can smoke a filter pipe without a filter or adaptor, and most smoke just fine.
I agree, let your mouth heal, and try again, cautious, judiciously. You may become more sensitive to flavors if you aren't smoking so hard.