Been out of the loop for a while, am subscribed to this thread (for the Z1ES though) Here's my 2c for what it's worth:
Regardless of my specific recommendation below, I'd keep 2 things in mind (apart from the obvious, listen to the speakers in person if you can at all...):
1) don't expect special "synergy" just because the speakers are the same brand as the HAP-S1. Sony is not a brand known for their speakers, and while the above-mentioned, rather expensive ones may be perfectly good, things quickly change when you get to "budget" pricing (and speaker-wise the SS-HA1/SS-HW1 would fall into that range, sorry to say) So for that same price range, there might be other non-Sony branded speakers that might be a great match...
2) Considering that, and the fairly low wattage of the HAP-S1, which probably also can't be pushed hard without distortion (since it's not the focus of the HAP-S1, which is being a great DAP, with the speaker output being more of a convenience feature), I would look towards tube-amp-friendly bookshelf speakers since they are designed from the ground up to present an easy-to-drive load to the amp as well as be very sensitive, thus requiring less power to get a fairly big sound.
I'm not sure where you're located, but I looked at a number of them from various parts of the world, at a fairly reasonable price (and alas I don't know what your budget constraints are) One drawback may be that you usually can't just buy them off the shelf, but the patience may be rewarded.
Personally, since my budget was pretty tapped out after getting a tube amp, I went for bookshelf speakers first to save for something nicer ones later. I ended up with Zu Audio's Omen Bookshelf speakers, and I couldn't be happier. Well I could when I'll buy one of their pricier floor-standing model, a no-brainer for me considering how much I like these already. Not sure if allowed to link to outside vendors directly, but you'll find them easily with a web search.
Their spec pdf is fairly detailed, but in essence they are 12 ohm (the HAP-S1's spec permits 4-16, and consider that the lower the speaker's impedance, the more power they require to be properly driven) but more importantly have a 97dB/1W/1m sensitivity which is much higher than your typical speaker, allowing for as little as 4W to run (up to 200)
This is just one example of this type of speaker, but I honestly really like Zu's voicing, which is fantastic for singer-songwriter, acoustic, chamber etc., and not bad at all for everything else. Well, perhaps not ideal for hard-rocking metal or deep-bass electronica (though make no mistake, they can get loud when needed) One thing to be aware of, even after reading the measurements: when I got them, I found them to be rather big & heavy for "bookshelf" speakers, it was really at the limit of the shelf I have them on for now.
Anyway, maybe at least some food for thought...