problem with ph neutralizer

I've been having a problem with (what appears to be) calcite particles appearing in my toilet tanks and bathtub. I have an upflow ph neutralizer system.
First I installed a reusable sediment filter on the house side of the ph neutralizer, but it clogs up too frequently.
I talked with a local filter guy that told me that my ph tank head probably didn't have a filter on it (which it didn,t) so he recomended replacing the head with a one which incorperates a filter (which I did).
Now, whenever we fill the bathtub, it clogs up the ph tank head filter and reduces flow to a trickle. Even if I fill the tub up slowly I still get some sediment in the sediment filter down line from the ph tank.
My regulater is set at 40-60 and tank at 38. I have the calcite top level at 16" from top of 10x54 tank.

Would a downflow system take care of this problem?

I talked to an online supplier who suggested using a Fleck 2510 sxt on a 10x54 tank calcite only.

Would this system be adequate?

I have a 1" supply which feeds the main house (3 to 4 people 2 1/2 baths) and a cottage (1 person 1 bath). The pressure tank is fed from a 1500 gal. holding tank with a 20 gpm pump.
Well recently tested at ph-6.5, iron-0,mag -0.041, cloride -100, hardness -4,alk -4, tds -55 .

Also, the tank is located in the well house which is outdoors and no convenient drain.
Since I'm only adding calcite to the water, can I drain to the ground?

You could use a down flow system but I would recommend a fleck 5600 flat cap, (filter valve) It will also be okay to backwash onto the ground outside. Also if your hardness is 4gpg before you added calcite it is probably around 7+ now. Your tank size is okay but perhaps you may want to take out some of the calcite first before you start adding or changing anything. I would measure your ph and see what it is as well as your hardness. If ph is too high then take out some calcite, you may only need one cube and it sounds as if you have almost 1.5 cu ft of calcite.

Thanks for the response. I will consider the Fleck 5600.
Another question... I currently have a 2 3/4 x 20 20 micron sediment filter before the media tank. I was advised to go to a 4 1/2 x 20 75/25 filter ( which I purchased but have not yet installed ).
Does this sound like good advise or is it even necessary to use a sediment filter if I switch over to a downflow system which is periodically backwashed?

I am usually frugal when it comes to putting on filters, do you know what it is that you are filtering, if it is sediment like sand you would want to use the one you have been using and put it in front of the calcite filter because the sediment will wear down the filter piston sooner than you want it to. Hope this answers your question