Not building up a set of constraints together with the possibilities in a language can result in over-extended creativity. Presumably you have chosen ἠλιθίως for the nuance of “not suspecting that something is amiss” or in a “good” sense, " who doesn’t know what they’re missing ".
The lack of a style and usage manual of Greek is partly to blame there. An example is the recent εὐδία ἔχει discussion - how can one know what idiomatuc usage there mught be. Currently available resources to help with composition are quite inadequate, so even if those those who ἠλιθίως παίζο[ντες] “play without being aware that there are rules to be followed” came to the point of realisation that freedom has constraints, it would be difficult for them to find what the contraints are. One of the resources that seems to offer hope in regard to εὐδία ἔχει is sections 40-49 of ἔχω (intransitive uses) in the forthcoming Cambridge Greek Lexicon. Have a look at Emeritus Professor James Diggles short duscussion at about the two minute mark of this You tube video. The unreferenced paper version won’t be so much use as the electronic version with links to perseus. If the electronic version allows one to isolate all the intransitive uses of ἔχω, and specifically those examples where it means “continues (to be)”, then it coukd be easily seen whether there are examples in their corpus of 70 authours where it is used without an explicit or implied adverbial complement.
The other obvious problems in composition is rendering of the wide-ranging English modal system and things like “probably” and “room”, that have so many different (non-analogous) way to be expressed. The preference to develop meaning analogously by function rather than form is also somewhat askew to the expectations of English speakers.
It is interesting to see how attempts at composition fall short of the ancient authours. The discrepancies are quite patterned.
[For the purposes of composition, the complete lack of any Greek at all in the definitions of the forthcoming dictionary will probably result in the improper collocation of Greek words that happen to have the same glosses in English. ]
There are basic everyday things you need to fix. E.g. in your first sentence here: position of τε (should directly follow τά), τὰ τῶν ἀρχαίων γραφέντα ungrammatical, τὰ τῶν νῦν ὁμιλοῦντα meaningless, and more.