LO,
The trouble with your favoured version of the F-35 is that LM aren't building it and no one else is saying they need it. Hence, you are making an already expensive aircraft even more expensive. As this would be just your requirement you would be expected to front up all the costs for design, development, test etc adding further to the cost. Bottom line is that none of the partner nations would be able to afford it.
If you want probe and drogue without the lift fan you have to buy the C, or an F-18/Rafale etc.
On the point of single engined jets strafing targets, GR7 and 9 did it quite successfully in Afghan for a fair while, all be it with rockets rather than a gun. The number of engines was not an issue.