Small Pipe and Relights

How do the diameters compare? Less surface area for combustion requires a slight change to cadence to keep a similar burn temp to a wider bowl.

Could be myriad of causes for the relights, packing, tempo, tobacco, tamping. I'd start with packing the pipe. Pay careful attention at first, checking the draw and the spring of each level or tier. Is the tobacco nested with a bit of spring. I'm one of those who believes blends are sold ready to smoke. Perhaps it's the blends I smoke. Too we will smolder unevenly. When I pack I gently twist my finger a bit to nestle the blend with plenty of air space. Tight enough to feel the draw, light enough to provide for ignition.
During the smoke, if the need for tamping arises, I spin the tamper, my finger, a bit as I press gently. My personal belief is "nesting" the tobacco creates a better burn as opposed to just pressing the load down. Are you tamping the oxygen out. Tamping too tight makes it hard to keep ignition. I smoke pretty much unconsciously now. Years ago I had to pay attention so to keep the oxygen available for combustion.
To find the answer(s) you are going to have to "parse" the experience for a while. Start with the obvious, too much and too hard a tamp. Perhaps you're depriving the burn of oxygen. Then work logically though the experience and see where you might be failing to provide what a burn needs, oxygen, combustible material and heat. Using the finger to tamp means a light twisting tough with the finger. Too much pressure, too much time pressing and even the calluses won't protect my finger tips from a bit of pain.
It's easy, just takes a bit of attention and logic.

I don't think the diameter nor depth of a pipe matters as much as how familiar I am with how that specific pipe wants to be smoked. I have fat pipes, narrow pipes, medium pipes, tall pipes, and squat pipes, some I know well and always smoke straight to the bottom with no relights, and some I am still figuring out.

My motto is that there are no bad pipes, just some pipes have a steeper learning curve.

I don't think the diameter nor depth of a pipe matters as much as how familiar I am with how that specific pipe wants to be smoked.

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We all have a unique smoking style that we frequently vary with the pipe. In my case, the variance is entirely accounted for by the difference in airflow of which bowls dimensions are a good part. But, this may have nothing to do with the OP's issue.

Hmm, you may be overpacking. Try packing lighter first. The tempo tends to work itself out when the pack is right.

I guess what I mean is different blends sometimes require different pressures when loading. Obviously what you are doing with your larger pipes is not working with the smaller bowls. You will have to potter around a bit to find what works. Might be fun! You are sure to learn something new about your pipes.
edit: 20 members will give you 15 to 20 different suggestions. Just try some of them and see what works for you.

I put my two fingers over the bowl creating a "forced enhanced draft" more frquently

I haven't noticed that so much, however, I have found that flake or plug goes longer in a small pipe than loose tobacco with fewer relights.