Just by chance, I have an article on this topic.
Your polishers DOES have a spindle. You do need a PC wrench. If you don't have one, a 9/16 U.S. or 14 metric will work but it has to be a very THIN wrench. and if you're in a bind, (no pun intended), you could take a 9/16" wrench and using a bench grinder, grind that sucker thin and flat.
Or if you have a PC wrench, using your eyes, peek into the housing and locate the COUNTERWEIGHT - bring the wrench in from the OPPOSITE side of the counterweight as they is a LOT more clearance room for the wrench. Then having a buddy help you, someone hold the tool and the wrench and then take a HAMMER and MAKE the wrench fit onto the spindle. Then twist off the backing plate.
Here's one of my articles with pictures to show you what you need to do.
I don't know if this will help but I took a whole lot pictures and this will probably become the "Definitive DA Style Polisher Wrench Thread"
Without further ado...
BRAND NEW WRENCH OUT OF THE BOX OF A BRAND NEW 6" GRIOT'S GARAGE ROP
As you can see, it fits the Free Floating Spindle Assembly perfectly and this wrench has a little hole in the end of the handle were you could hang it up on a peg on a peg board in your garage. (I should have taken a picture of the entire wrench).
Same exact wrench on the Free Floating Spindle Assembly of a Meguiar's G110v2 - It fits snug and perfect.
Drumroll..... The brand new factory wrench, just out of the box does NOT fit on the Free Floating Spindle Assembly on the Porter Cable 7424XP. It could if I muscled it on, but it definitely does not SLIP on to the hex head exterior of the FFSA.
I have placed the brand new wrench out of the box onto the housing on the Griot's Garage ROP and now have a wrench that "someone" has abused a little, and the span of the opening on the wrench has been stretched by abuse and not only does it fit on the Free Floating Spindle Assembly of the PC 7424XP but it's a little loose.
Same picture as above but a close-up view and you can see the free space between the wrench and the Free Floating Spindle Assembly.
Just for fun, here's a 15mm wrench on the PC and it's loose - you need 14mm
Tested out a 9/16 and it fit onto all three Free Floating Spindle Assemblies... Didn't check a 14mm as I have one more project to do before I can leave for the day.
I realized a standard or metric wrench is too thick to attach a backing plate to a tool, the above pictures with the metric and U.S. wrenches was for perspective only.
I personally have a 9/16" inch flat wrench probably from the 1960's or older that I use to tighten down the bolt that holds down a Chevy Distributor because it's bent and ti also can be used for DA Polishers because it's very flat.