Nurseries often sell espaliers on the wrong rootstocks and/or of the wrong varieties to be productive in a small space, so you can't assume your problem is entirely about how you are pruning.

I think you should search further for information on pruning espaliers than the link given. It makes it look very simple but doesn't even explain that espaliers are maintained primarily through summer pruning.

Some varieties you can get to form flower buds by repeatedly cutting new shoots during the growing season to short pieces with just a few leaves while other varieties you need to leave the weakest shoots uncut until they produce flower buds.

See the excerpt from "Fruit Grower's News
___"Any summer pruning should be accomplished after the apical bud sets. If shoots are removed before terminal bud set, expect to see re-growth near cuts. Excessive early pruning can also reduce conversion of shoots into spurs and delay or inhibit flower bud initiation."__ ( see the link below)

PLEASE NOTE that espaliers are pruned differently that regular trees. So next spring and early summer you can keep pruning off the new growth through early July. Next year you should prune the new water shoots and growth to maintain the shape of the espalier and to keep it open and airy.

There are many videos on Youtube that discuss "summer pruning espaliers".

My espaliers are young and still growing vigorously so the get pruned in late May, early July and September.

Good Luck

Mike

Hard to say from the pictures but it does look like what my McIntosh (non-spur) was doing and trying to get a spur but the constant pruning would turn them into branches until it eventually had no fruiting spurs. (3rd picture down)
It took the late summer pruning to get it back to fruiting. As long as I leave it over grown the spurs will stay spurs quite a while.
So now I'm trying to thin the over growth back a little each year without shocking it into trying to make everything branches again.

Timing that late summer pruning is the issue, again coming down to not knowing the variety making it difficult.

Repetitive cutting of shoots during the growing season stops some varieties from setting fruit buds, but other varieties respond differently based on what I've read and my experience with certain pears. (Mike, I told you that your problem with the method is you were performing it on Macintosh which tends to set flowers on 2-year wood- for it, repetitive pruning creates a purely vegetative response.)

You can also prune espaliers anytime during the growing season for any variety if you are only removing the more vigorous shoots- not just water sprouts (as stated in the article).

There are several other things in the article I could debate, but a short article has to speak in sweeping general recommendations. Pruning espaliers involves much more aggressive removal of wood than regular "3D" trees, even if there is some overlap in potential response.

One rule of thumb for espaliers in particular, feel free to remove any shoots or branches off a main branch that is more than a third the diameter of that branch at the point of attachment- and do it at most any time.

The fruit almost always sets on the less vigorous shoots and with espaliers relative diameter is the primary determiner of vigor. With free standing trees branch angle and position in tree (light exposure) is also important.

The replacement espaliers were grafted and selected by me with the intention of them being espaliered by comparing my spur Cortland to the non-spur McIntosh.
If I hadn't lost my free standing McIntosh this year the espaliered one probably would be either cut down or pruned without a care if it fruited.

One of the others is a spur Mac so once it's bearing full I can play around with the stubborn one.

The part I quoted tracked most of the info I've read at various extensions and books and also in one of the Dave Wilson vids.

As you noted, espaliers are pruned differently.
The one consistent bit of advice to promote feuiting spurs is to prune the water shoots to a stub as described.

Mike

Red Delicious has an annoyingly vertical growth habit that is an odd choice for espalier, but can be done.