Abandon centrals early. Go for an extremely aggressive remote game, rush out agendas like there’s no tomorrow. Naked campaigns early are usually fine because Lock Hayley doesn’t really have the tools to reliably contest them. Your goal should be to get to at least 4, ideally 5 points by the time they’re set up. Then you can start icing up R&D some more, shove something into your remote every turn ideally, and force them to run it a lot. If you’re on match point and they are not, it’s often worth putting the winning agenda in the remote even if you know they can get in. Sometimes they’ll psych themselves out and not run it, and either way you force them to waste resources.
Another nice play is to build a second remote. Not as big as the primary scoring remote, but just 1-2 ice - something like Architect --> FC3 is great. Then, if you’ve managed to get to the point where you’re on match point and they’re not, you can shove into both remotes at once. Hopefully they’re both agendas and then they have to get into both or you win, but even if they aren’t both agendas you can at least force them to either get into both or guess right.
Beth will give them free clicks, you should accept that and move on. I don’t think it’s worth trying to play around that. If you’re looking for a current that’s good against Hayley, Scarcity of Resources is better than ELP. Also might be worth swapping a single Ash for a Corporate Troubleshooter. Sneaky Corporate Troubleshooter can mess with their Faust math, and it gets around Rumor Mill.
I’ve played this match-up a lot, feel free to PM me if you have any specific questions.