[Triarii]

I suspect that the basket hilts were more like the bottom right photo above. The contemporary illustrations show an evolution of hilt shapes towards more complete basket hilts by the early C17th. The slightly later Basing House (1645 at latest) and Sandal Castle swords (1646 latest) are very much like the bottom right example. Sandal Castle sword is below (the rusty one) and also my c.1620 version, very similar to both those siege finds.
I'll go digging, but basket hilts were recommended for forces sent to Ireland and for the militia.

In 1614 the London Cutlers Company were supplying 'Irish hilts' and 'open hilts' suggesting again that Irish hilts were close hilts.

Francis Markham, writing in 'Five Decades of Epistles of Warre' in 1622 (he was also the muster master for Nottinghamshire so should know about military matters) recommended swords with 'the hilt of basket fashion, round and well compact', which I take to be the fully developed basket hilt. He also says that musketeers should carry a sword 'with a basket hilt of a nimble and round proportion after the manner of the Irish'.

Portraits from the 1640s and 50s attributed to Colonel Hutchinson, Colonel Booth and one of Edward Massey all show (higher quality) basket hilts of the more developed form but not significantly different from the 1620s form, though flatter bars have become more the norm.