So to answer your question.... no.
You need to remember what you've purchased is a Dublin - New York fare, you can't segment it out as you've suggested, at least not on a filed thru fare.

Doing what you're suggesting will typically involve repricing the ticket into a higher fare that does allow the combination or 2 separate fare components (DUB-LHR + LHR-JFK) which is more than likely going to be mote expensive than a DUB-JFK in Club fare difference (the one offered to you).

I'm presuming you're currently booked into T class for the LHR-JFK sector which books specifically into certain Economy booking classes only for the short haul connection. If you'd selected the E Class (mid range Premium Economy fare), these usually book into I class (Club Europe) for the short haul connection.

You could try for an airport upgrade (AUP) on the day for the DUB-LHR sector but there's no guarantee an offer will be available.

If you're not up for paying to upgrade the existing New York ticket and don't want to leave the AUP to chance, why not just take a day trip to London at some point before your status end date? DUB-LHR-DUB can be had from around €80rtn on BA earning 5 tier points in each direction.... which will achieve the TP's needed.