There are, to my thinking, only a couple ways to keep a nominal half-inch plywood as the first layer over the joists for use under a ceramic tile installation.
A. You pretend it's not even there and install over it a layer of at least nominal 3/4" T&G, exterior glue plywood with no face of grade lower than C, fastened to the joists.
your existing plywood is in nearly pristine condition and very clean, you can glue-laminate another layer of nominal 1/2" exterior glue plywood over it, using a full spread of wood glue and many screws.
On top of either subfloor you can install the tiling substrate of your choice and your tile.
You don't need a medium bed mortar for any of you applications in this project.
When looking at the bonding mortar bags to determine what's in them, pay little or no attention to the words modified or fortified, which are used interchangeably and are equally nebulous. What you want to find is a number or numbers. To qualify as a "modified" thinset mortar the bag will say the contents meet the requirements of ANSI A118.4 when mixed with water. If it doesn't say that, it's not a modified thinset mortar. It may say it also meets A118.11, which is only important to you if you're spreading it on plywood, but it does indicate a higher quality than a mortar that meets only A118.4. So look for the A118.4 if you're wanting a modified - or fortified - thinset bonding mortar. The one that says medium-bed will also say it meets that same standard if it does.
It would help with some questions if you would put a geographic location in your User Profile for our folks to see.
My opinion; worth price charged.