I have also been learning how to summer prune in the last few years,
and have made a lot of mistakes. I planted trees very closely (e.g.
full-sized apricots, plums, peaches, and pears at 2-3') and so I
*really* need to summer prune! I never tie down limbs, no time to do
that on all the trees I have. In the summer I primarily hedge back --
I have some battery-operated hedge trimmers and I can hedge my 400
trees in one hour. I do this around three times in the summer. My
goal in hedging is not to take off 1/3 the new growth, but to take it
back to about 6"-1' of new growth. My plums have already put on some
2-3' shoots up top this time of year, and taking off just 1/3 is not
going to do much. If it is looking too "dark" inside the tree I also
do thinning cuts - take out a big long limb. I also look at the
spacing between the larger limbs. At something like 2-3' above a
joint I like to see the limbs 1' apart, and higher up I like to see
the limbs 2-3' apart. It took me some time to get this correct
balance in my head, but now I have it and I just remove until that
proper level is achieved.
I have the same problem with the multiple shoots. In the winter is
when I thin those guys back, if four came out I pick one or maybe two
to keep. I also do a lot of more major thinning in the winter so many
of these multi-shoot clusters are removed completely. I have been
trying to transition to do more summer thinning -- when the leaves are
on I can see better where to thin (look for the too-dark interior) and
also there is less strong a flush of new growth than with winter
thinning.
Your Toka plum sounds like my Howard Miracle plum. It produces
millions of tiny shoots from everywhere. It has been one of my
hardest trees to prune, and very prone to diseases partly because of
the subsequent lack of air circulation. I believe the way to prune
such a tree is to have extremely wide spacing on the major limbs to
compensate for the large density of shoots, and to thin out the shoots
as best as you can.