Specifying a Phrase within a Proximity Phrase Search?

I'm using the a Query String Query to perform a Proximity Search.

I'm wondering if ( and if yes how ) I can nest a phrase within the overall
"wood glue manufacturer"~5 ( where "wood glue" would be kept as a phrase )

My users have access to a Query String Query box and I'm exploring more
advanced search capability through this box ... so performing the
equivalent with other Query types is not helpful here ... for instance, I
know that I can use a Span Near Query to accomplish this.

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Have you found a way? I think the span is the only way to do it. Which is unfortunate because it requires complicated parsing of users' queries. Please post if you found a way!