I don't think either Purigen or Chemi-Pure will do much, if anything to reduce nitrate. They are great products, but reducing nitrate really isn't what they are for. IME & IMO; most artificial products called "nitrate reducers" don't work. What product are you using?
I really like Aqua-Clear filters and have used them for different jobs for about 30 years. I had one that ran non-stop, except for a move, for 25 years. Their foam blocks are big, not little pads combined with cheap carbon. They are very easy to rinse every day or so--they hold an incredible amount of crud. But, in some set-ups the foam block actually become a main culture spot for aerobic bacteria and rinsing one can cause a problem in small tanks.
I agree with Henry, a box filter usually isn't a good place for crushed LR; but what else do you have for reducing nitrate? Any LR? If you need a little help short-term; you can keep the media bag of crushed LR on top of the foam in the AquaClear. That is back-asswards, but will keep most crud away from the crushed LR. Keeping nitrate low in a small tank can be tough. A small bio-load, aggressive water changing, and enough LR is the only way I know to do it. BTW, is this a reef or fish-only tank? Fish can handle nitrate at 60ppm with no problem (IMO&IME). Inverts are another story.