I have an [name]Imogen[/name] who is 2 now and her middle is a floral: [name]Lily[/name]. Like you, I wanted to lighten the buttoned-up feel of [name]Imogen[/name]. Florals and other light names go great in the middle with [name]Imogen[/name], IMHO.
As for nicknames - we have a long list: [name]Immy[/name], [name]Imo[/name]/Imma, [name]Gen[/name]/[name]Jen[/name], [name]Mimi[/name], [name]Mo[/name], Momo, [name]Gemma[/name], [name]Minnie[/name] (we don’t use them all at this point, but I like to “collect” them so that as she grows if one fits her we can use it… and I’m pretty comfortable stretching for a nickname). We use [name]Immy[/name] mostly with the occasional Imma and Immaboo/Immabee/Immabelly strictly for fun.
Our experience with the name might be skewed by where we live - in the south of the US - where there seems to be about zero recognition of the name. We get “oh, like imagine?” a lot. We also have had, “like imaging, you know, imagin’” and a couple of older people have said, “Oh I haven’t heard [name]Imogene[/name] in a long time.” Of course, when we go visit family in the UK, there is 100% recognition of the name - no one is confused or needs it repeated. I’d guess that any little [name]Imogen[/name] in the States will likely have to spell and repeat her name a lot - but it’s such a fantastic name, it’s worth it! Hopefully she’ll feel the same way about it.
Good luck naming!!! You clearly have fabulous taste in names