Home Depot and Lowes plywood is crap. Find a real plywood supplier. The Wurth Group is one of them and they have locations all over the country. If none near you, ask a local cabinet shop where they get their plywood. Independent lumber yards that cater to builders even have better plywood than Home Depot and Lowes. Usually at better prices too. For cabinets, I always buy 3/4" Birch Cabinet plywood. It's even really 3/4" thick, with one good side and one with maybe a few small plugs. A/B quality. The last that I bought was $38 per 4X8 sheet. This stuff is a giant step up in quality from the Home Depot and Lowes junk. It's even flat. I've never found any metal in it either, and have several times with plywood from Lowes. It's really sickening when you hit metal with a nearly new $140 Forrest Blade.
Solid wood for making a face frame, even one that only covers the plywood end grain, can be made from poplar and produces good results for painted cabinets, or if you will be staining the cabinet, soft maple is a very close match in color and appearance to the birch used in the surfaces of the birch plywood. I use it frequently when making cabinets from the birch plywood. It isn't as expensive as hard maple either, usually running only slightly higher than poplar. Wherever you get the plywood usually has hardwoods too. Buy from them, not the big box stores. You will get better quality at lower prices. It's outrageous what Lowes charges for poplar, maple, and red oak hardwoods.
Use shims or make your toe kick area slightly different for the height difference. It will be less likely noticed there. For 1/4", just shims will be enough, Then apply a small molding to both to hide the shims and make the appearance the same.
The cabinets that I've been making over the last few years have been for the NC Science Museums and are custom made Exhibits Cabinets. I do everything from concept to completion of the exhibits including electrical, hydraulics, pneumatics, programming, etc. but I don't do the graphics. They have a department for that. It's sometimes quite a challenge.
I volunteer my services for this. I'm a retired EE Automation Engineer that once created control systems for large scale high speed integrated circuit manufacturing.
Charley