Not always easy to get things growing under beech trees, as you know, due to the chemicals in the leaves but you do seem to be doing pretty well in spite of that.
Native bluebells should do well there and should spread well if left to their own devices, as will snowdrops and maybe wood anemone, sweet wooddruff and red campion.
I have a couple of areas that I let grow long until the flowers have finished, in these areas I've grown : orange hawkbit ( not a true native but looks great and wildlife friendly), also oxeye daisy and ladies bedstraw are increasing well. Some primula's grow well there too.
I like to plant in small drifts, then allow nature to do the rest.
Nice project, good luck with it!