The second half of the bowl

If you need many relighting it is likely a too humid or too packed baccy. Try to dry it more and pack it lightly.
About that you enjoy more in the second half you will find likely most of the people including myself that they prefer more the first half because in the second half you could start to taste the ashes (you can diminish this emptying the ash half way) and also the bottom tobacco get soaked with moisture and tar and get acrid. If you don't like too much the first half again probably it is because it is too wet or packed too tightly.

Dry the tobacco out to the degree possible. In humid N.C., we have to have air conditioning or move to the coast or the mountains, or so it seems. In Massachusetts a.c. used to be pretty rare; I'm not sure about now. At least pack the pipe and let it sit overnight or dry out a few bowls in a crockery bowl or whatever. Also, tamp between relights attentively, but don't pack it down too hard. You need air through the blend. You're right, the second half of the bowl, until you get right down near the bottom, should be about the best. But when the taste gets acrid/harsh/lame, let it go out and scoop it out, and start over.

Isn't it somewhat normal to have to relight more often as the bowl is in the last half/last quarter? I know it is for me. Granted, I'm a relative novice myself. I try not to worry about it too much.

I believe Boveda makes lower RH humidity packs intended for things other than cigars. You might want to experiment with those. For example, if you have some tobaccos you know you will smoke over the next few days, take enough for a few bowls of each, place them in unsealed plastic baggies (to keep separate), and store them all in a tupperware or something with a Boveda pack.
Boveda Product Range by RH

If the blend has Virginias in it, I always prefer the second half of the bowl. The sugars in the tobacco get stoved and cooked, and it brings out some caramel and brown sugar notes

dani', I haven't seen it discussed on Forums, though it may have been, but if I divide a pipe bowl in thirds, I think the second third burns with the fewest relights. The top/first third often needs a relight or two to get it to even up. The last third begins to run out of tobacco. The middle of the bowl should be a relatively steady burn for the ember in many cases. This is just my experience. Some bowls go right to the bottom, with good taste, with the right blend in the right pipe.

Lloyd, I live on the coast a few miles south of you and had the same problem. Good advice here. I found that I was drying tobacco out too much, which seem to make it hotter and less flavorful. I'm only having trouble with Samual Gawith flakes now, which are infamously wet. The HH Mac Baren flakes used to be a real problem for me and now I've taken up folding and stuffing method, right out of the tin and it works fine. The key I found was not tin moisture (barring SG) but packing too much in. I'm loosely packing 1/2 - 2/3s of what I used to and it burns longer and with many fewer re-lights. I was greedy packing the bowl and tossing out clumps of wet tobacco after 25 min, rarely burning ash to the bottom. Start really light loads (as above) and work more in to suit pipe and tobacco.
English blends seem to burn more easily and cooler and I will steal the suggestions from this site that worked for me, Westminster and Artisan's Choice (sweeter) if you'd like to start back in English/oriental blends. Pease has good variety of other English blends that you may like.

If the blend is Virginia forward I usually am enjoying more the second half whereas with the burleys this seems to be opposite