Not yet resolved, however I followed queasd's prescription (slightly emended).
LOCAL_VERSION is set with extension=25.10.11.
make; make modules; make modules_install; kinstall [queasd]
This resulted in the creation of:

/boot/vmlinuz-2.6.29.6-smp-25.10.11
/boot/System.map-2.6.29.6-smp-25.10.11
/boot/initrd-2.6.29.6-smp-25.10.11
/lib/modules/2.6.29.6-smp-25.10.11/

and the lilo stanza is

# Linux bootable partition config begins
image = /boot/vmlinuz-2.6.29.6-smp-25.10.11
initrd = /boot/initrd-2.6.29.6-smp-25.10.11
root = /dev/sda5
label = Slackware
read-only # Partitions should be mounted read-only for checking
# Linux bootable partition config ends

However on booting to this kernel errors are received as follows

.....
initrd-2.6.29.6-smp-25.10.11: Loading kernel modules from initrd image
Using /lib/modules/2.6.29.6/kernel/fs/mbcache.ko
mbcache: version magic '2.6.29.6 mod_unload 486'
should be '2.6.29.6-smp-25.10.11 SMP mod_unload CORE2'
insmod: cannot insert '/lib/modules/2.6.29.6/kernel/fs/mbcache.ko'
Using /lib/modules/2.6.29.6/kernel/fs/jbd/jbd.ko
jbd: version magic '2.6.29.6 mod_unload 486'
should be '2.6.29.6-smp-25.10.11 SMP mod_unload CORE2'
insmod: cannot insert '/lib/modules/2.6.29.6/kernel/fs/jbd/jbd.ko'
Using /lib/modules/2.6.29.6/kernel/fs/ext3/ext3.ko
ext3: version magic '2.6.29.6 mod_unload 486'
should be '2.6.29.6-smp-25.10.11 SMP mod_unload CORE2'
insmod: cannot insert '/lib/modules/2.6.29.6/kernel/fs/ext3/ext3.ko'
mdev: /sys/class/scsi_host/host4: No such file or directory
mdev: /sys/class/scsi_host/host5: No such file or directory
Trying to resume from /dev/sda6
PM: Starting manual resume from disk
mount: mounting /dev/sda5 on /mnt failed: No such device
ERROR: No /sbin/init found on rootdev (or not mounted)
Trouble ahead. You can try and fix it. Type 'exit'
when things are done.
/bin/sh: Can't access tty: job control turned off.
#

and the console is frozen. For some reason the loader is trying to access
the module tree 2.6.29.6 (which does exist) instead of 2.6.29.6-smp-25.10.11
There may be other errors.

I feel I'm almost there (encore un effort) but need a final illumination

Looks like you didn't build an initrd for the new kernel/modules and it's using the old one.

Well, I believe I did:

LINUX_SOURCE_PATH=/usr/src/linux
IMAGE_PATH=arch/x86/boot/bzImage
INSTALL_PATH=/boot
cd $LINUX_SOURCE_PATH
KERNEL_RELEASE=$(cat include/config/kernel.release)
# Install modules and the image, build initrd.
make modules_install
cp -v $IMAGE_PATH $INSTALL_PATH/vmlinuz-"$KERNEL_RELEASE"
cp -v System.map $INSTALL_PATH/System.map-"$KERNEL_RELEASE"
cd $INSTALL_PATH
mkinitrd -o initrd-"$KERNEL_RELEASE" -k "$KERNEL_RELEASE"

-rw-r--r-- 1 root root 915614 2011-10-25 21:07 initrd-2.6.29.6-smp-25.10.11

Add the -c option to clear out the old initrd
mkinitrd -c -o initrd-"$KERNEL_RELEASE" -k "$KERNEL_RELEASE"

You didn't add necessary modules to the initrd, it seems. That is the whole point of it, putting the drivers in it that are not compiled into the kernel but necessary to access the disk(s), like file-system drivers or drivers for your disk-controllers. Or mdadm if you want to start a system that is residing on a RAID.

That removed the insmod errors during boot, thanks colorpurple
Now I am left with:

mdev: /sys/class/scsi_host/host4: No such file or directory
mdev: /sys/class/scsi_host/host5: No such file or directory
Trying to resume from /dev/sda6
PM: Starting manual resume from disk
mount: mounting /dev/sda5 on /mnt failed: No such device
ERROR: No /sbin/init found on rootdev (or not mounted)
Trouble ahead. You can try and fix it. Type 'exit'
when things are done.
/bin/sh: Can't access tty: job control turned off.
#

after which the console freezes. I googled the mdev error but with no success.
sda5 is the boot partition. Any further suggestions? Must be close now

It seems that it is lacking a driver for your harddisk-controller.

Where do I look in the kernel configuration?

in a terminal run /usr/share/mkinitrd/mkinitrd_command_generator.sh to figure out what modules need to be loaded into your initrd.

There are two possibilities:
1. You haven't compiled a driver for your hardware at all, change that in your kernel configuration. i don't know which driver you have to activate, since I know nothing about your hardware.
2. The needed driver is compiled as module and has to be integrated into the initrd. Again, that is the whole point of an initrd, besides from some exotic uses for it.
Try the command suggested by colorpurple21859 and look if that helps.

The result was:

mkinitrd -c -k 2.6.29.6-smp -f ext3 -r /dev/sda5 -m usbhid:ehci-hcd:mbcache:jbd:ext3 -o /boot/initrd.gz

The only module missing is usbhid, and it's true that I disabled HID in the kernel configuration
since I was not familiar with it from previous installations. I'm recompiling now and hope for
a good result...

I am learning quite a bit from this thread, and I have a few questions of my own.

When exactly is it a good idea to clear the initrd tree with -c? I've never done this before, but everything seems to work just fine.

Is there a point in using initrd if I don't add any modules to it with -m?

If you have all your needed modules to access your hard drives and file system compiled into your kernel instead of as a module then you don't need a initrd. I usually compile the drivers I need into my kernel so I won't have to be bothered with generating an initrd. You need to know your hardware to know what drivers are needed. I believe you need to clear the initrd tree whenever the kernel version changes.

The Kernel God be praised. It worked

That is, after executing

mkinitrd -c -o initrd-"$KERNEL_RELEASE" -k "$KERNEL_RELEASE" -r /dev/sda5 -m usbhid:ehci-hcd:mbcache:jbd:ext3

I was able to boot to the new kernel (there is still a minor issue with the nvidia modules).
I'd like to offer my sincere thanks to all who have helped resolve this problem, and especially
qweasd for kinstall, colorpurple and TobiSGD.

What is particularly pleasing is that my original question is also answered: with this setup
I am now able to boot alternative kernels from the same partition simply by selecting the
appropriate one in the boot menu. No need to adjust symlinks etc prior to rebooting.

I take your point, colorpurple, about compiling drivers for the file system and hard drives
into the kernel, thus obviating the need for initrd. That will be my next step.

Praise "Bob".