Learning When To Dumb Out The Bowl, Signs Of Diminishing Returns

I'm cheap, and I want to get as much out of a bowl as I can. Is there a "rule of thumb" as to when to dump out a bowl and start a new bowl? or when I see white ash, I usually just cover it over with more and keep going, but sometimes I think I'm loosing flavor other times not.
So what are the signs leading to the point of diminishing returns, and I just need to dump it?
And when you dump out a bowl, do you leave the partially burned "embers" at the bottom of the previous bowl, or do you fully empty the bowl and repack it, or do you just start with a whole new setup?

(note that I still consider myself a newbie to the pipe)
So after a point, the top half of the bowl will have white ash that seems to be suffocating the un-consumed tobacco that still lies waiting at the bottom of the bowl. I say suffocating because my observation is that re-lights become more frequent and less smoke is drawn through the stem.
When I lay more tobacco atop the white ash, sometimes the burning of the new tobacco continues "ok", other times it does not help, and is difficult to burn, sometimes I'll stir it all up, which rarely seems to give desired results. Still, sometimes one of these methods works and other times they don't. Not at all sure, but I think these may simply be the relationship between certain tobacco cuts and a specific pipe? More often I dump the top half off (trying not to loose the tobacco at the bottom which is where I'm being cheap), and put the new atop, stir it around with a poker, run a pipe cleaner through it, re-light and hope for the best.
So I guess the motivation for my question is, should when should *I just be adding atop the new, or dump off the top (wasting), or stir it up (keeping), that the top white ash will help ignite the new tobacco laid atop, or in general loose flavor or gain me nothing?
The motivation for my question is of course retain the flavor of the smoke without wasting tobacco, but the answer to my questions are probably too general to make a blanket statement.

The whole bowel or just the top half?
I guess I'm looking for a balance between cheapskate flavor. Then again with an engineer mindset I'm probably way overthinking this.
Probably at his point in my "career" of pipe smoking, I should just go for flavor and dump it all.