Personally. I think because my NGTLD's get swamped by my GTLDs. I am considering splitting my NGTLDs off from my GTLDs. If somebody is looking to an NGTLD it's for one of two reasons. 1. They know there isn't something available in .COM (and no other GTLD will do), or 2. They want something more brandable which is more easy to obtain with an NGTLD. An NGTLD selling NGTLD's seems a logical choice, IMHO. eg, Brands.International.
I think we've become too fixated on the train of thought; using only .com for .com, or using only ngTLD for the new ones. We're not far off now where it simply won't matter- get a quality name and have it represent, no matter the extension.
I like your DNStore name btw; I think it makes sense as basecamp for any TLD. But that is not your question.
Have went the other direction than what you're proposing. I used to have two separate sites; one for my ngTLDs, the other for my ccTLDs and .coms/nets/orgs. Decided about a year ago to instead migrate most everything under one banner, using my ngTLD as basecamp. But, I have not experienced any benefit to doing this thus far, in terms of more sales. Though interestingly enough, much more inquiries on my legacy names landing under the ngTLD banner than before when based on my .com name.
It could be because my ngTLDs get a lot of interest, and having my legacy domains avail to explore at the same site people naturally gravitate towards them. So far everyone is playing nicely on both sides, seems kind of to be a win-win.
These are the NGTLD's which might be suitable IMHO. Domains, Online, Shop, Store, Website, Site, Business, Exchange, Services, Company, Direct, Works, Media, Digital, ForSale, Holdings, Ventures, Solutions, Market, International, XYZ, and Co (not an NGTLD). Are there any other likely candidates? Rank them in your top 5. And rate each of them for the same keywords how strong/weak they are as a percentage to the .com. (ie: Domains 20%, Store 30%).
Some of those I probably wouldn't consider- however as with all new gTLDs the right name can make any extension worth a second glance. Looking at probable connection/impact with audience though, and memorability, are my most important factors.
So, .domains being my top, then perhaps .store/.shop, .world, .global and .solutions is worth a real gander. I think Brands.International has made that ngTLD his, I would never use the extension but he has truly shown how an exception can stand out from the crowd.
I can see why you like .media, there's some great combos with it and a very strong TLD in terms of visual impact imo.
Rating these as a percentage to their .com counterparts, I think for the most part you really have to consider every name on an individual basis; eg. great fits vs mediocre pairings. Anything mediocre can't hold a flame to .com, .com=ambiguity, thus safety for lesser quality.