hmm have you looked at some of the post Op 28 Scriabin?
have a look and listen to lots of Poulenc's solo piano works, he had a huge output of solo piano music and they were 'smaller in scale', I wouldn't be super quick to call his sound 'impressionistic', his texture a lot of the time is neoclassical in style.
Percy Grainger. Wrote in a more 'tonal tradition' is often overlooked. LOTS of very pretty anch 'approachable' (for the listener) music from this period.
how about a 'Rachmaninoff' type sound (which btw why not some Rachmaninoff his preludes of op 23 are from 1901-1903?).
Heino Eller comes to mind too!
this piece from about 1917 (the crave) by jelly role morton (this recording is from a modern sound track and only about 9 seconds short of your two minute cut off but honesty a little rubato or almost undiscernable relaxation in tempo will get you there)
how about a movement or two from a kabalevsky sonatina, op 13 n 1 is nice, 1933
also, york bowen was much more rooted in the romantic tonal tradition, usually is compared to rachmaninoff in texture and sound, his earlier works will fit into your time period.
also have a look at William Baines
another beautiful set of 'preludes' (technially dainas 'folksongs') are the 24 of janis medins
ie
there's a bunch so look around for them, they are all on ty
you gave some decent parameters but there are huge variances in style as you can see I just sorts threw a few different examples, there is a lot and big constrast of styles available to you that fit your criteria.