I agree that you sound like you're on the right track.
I have recently started doing piano lessons with 4-6 year olds after many years of teaching older pupils. As you say, at least half the time is spent doing general musical activities as their little hands and concentration is limited.
I don't use it myself, but there's an american piano scheme for pre- schoolers which uses finger puppets, stickers etc called Wunderkeys. You could probably use it yourself if you can't find a teacher.
Other things I do with my littlies are
moving to a metronome beat/app,
making rhythms with one syllable sounds, clapping, tapping etc. They love my congo drums
Drumming while I play
Qs and As on the piano can be very funny and entertaining
Pupil improvising over an ostinato played by me z - requires no technical skill - this is very popular
Narrating an improvised piece of music
Singing our own words to melodies
Playing a story eg story involving a storm. Use of pedal, lowest notes for thunder, repeated notes for rain etc
Jumping on rubber floor discs according to pitch
Listening to chords held with the sustaining pedal. Very popular activity. Noticing when the high note finishes (ie before the bass note)
Playing tunes they know with 2 or 3 fingers either by rote, by ear or using the note names written down.
Playing the notes an octave apart using pattern of black keys to find the same note.
My advice is to negotiate with your DH to get a piano. It's surprisingly good for little ones. A keyboard would do at this stage if space is an issue. If cost is an issue you can often rent pianos from instrument shops.
Some schools in scotland do a block of ukelele lessons. You could teach yourself and do that with your DC.
As other pps have said, your nearest Junior conservatoire dept might do pre juniors from age 8 or offer summer holiday classes for littlies.
Final thought - how about dance classes. Great for co-ordination.