If the cost of either is acceptable to you, I would do the luxury speedboat trip and book an elephant trek yourself locally. The best one locally, I think, is Saurung Elephant treck whicxh takes you to a lovely waterfall which in June should be full of water. This is no more than a half-day trip. If you want a full day including an elephant trek/jungle trip, there's nowhere better than Khao Sok National Park. This would normally include a raft ride down the river which, again, because of the season will be more full than it is at the moment.
Have a look at Khao Lak Land Discovery, for instance, to give you an idea of options and prices.
Bear in mind though, if you go on the Lady Sarojin to Phang Nga Bay, although the Bay in June will be relatively calm, going along the coast from Khao Lak should be quite bumpy, so anti sea sickness pills might be a good idea. :)
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