I don't necessarily think that EZY have announced operations from SOU in a bid to force BOH to lower their landing fees.
I suspect it's more to do with SOU's location closer to London and the major conurbations of Hampshire and the south coast, it's increasing pax numbers and the withdrawal of Flybe from the more leisure-focussed routes after building up a demand for them, leaving a gap to be exploited. As others have said on the SOU thread, lack of Gatwick slots and a desire to eat into Heathrow's pax catchment have contributed too.
The Flybe situation was different in that SOU is a major base for them and a renegotiation of contracts may have saved them a lot of money at a time when they were struggling financially (still are!). The threat of opening a BOH base would have given them a large bargaining chip to use with SOU management, although that may have backfired in the long run with the BOH base being shut down and the flights moved to SOU, showing SOU management that no matter what Flybe said, SOU remains their priority and is way more valuable to them.
I honestly can't see that EZY would have gone to all the trouble of setting up a SOU operation purely to gain a small reduction in BOH landing fees, surely the cost of setting up at SOU would outweigh any gains at BOH?
Also, if SOU management do what's needed and actually invest airside, giving EZY adequate facilities to operate from, realistically what can BOH offer them instead, given SOU's far superior catchment area, transport links and momentum of passenger growth?