[Steam Inventory API] How to get appids for games you currently own cards of?

A bit of background

I use Steam Card Exchange a lot and I like their Watchlist function.

The problem is that it's hard to keep synched; i.e. to contain the exact list of games that I currently own cards for. Most of the time their will be games in the list I no longer have cards of, or games will be missing that I do have cards for.

So I decided to write a userscript to automatically synch up the list. It all worked perfectly at first glance...

The problem

Then I found out that the JSON file returned by this API: http://steamcommunity.com/my/inventory/json/753/6 is limited to 2,000 items. If you have more items then the JSON will end with: "more":true,"more_start":2000.

This basically scuppers the Javascript approach as I have to get the JSON asynchronously and can't do a second call (unless I cache it all in local storage or something equally involved).

The question

Does Steam offer a way to grab a JSON/list of games (appids) that I own cards for?
So it should not include games that have cards but which I currently have no cards for.

That list would be a lot shorter than the JSON with all cards as linked above. And all I need is that list; I don't need details on individual cards to synch.