Here's an interesting Forum post on the use of the Kongsberg autonomous underwater vehicles (AUV's) in searches "for the Electra, conducted in the general vicinity of Howland Island" by a couple of splash and sink groups.
I know the direct and support costs of tools like this are most certainly budget busters ("If wishes were horses ..."), but maybe Ted Waitt and the Waitt Foundation aren't using their UAVs and would lend them to TIGHAR

Ted was the founder of Gateway computers.
A UAV with the advertised capability would aid in sweeping out a much larger search area, probably at greater depths and with better resolution. Note that the nominal search area specification on the
Kongsberg website appears to be 1.2 sq. km per hour. A jpg showing an approximately 1 sq. km search area overlaid on the 2012 Niku ROV trails is attached. A crude back of the envelope calculation based on the specs on the Kongsberg website would suggest that the UAVs could image as good as a 2.5 cm resolution at a range of many thousands of feet. The calculation is based on round trip ping time subject to: "the platform cannot travel further than half the length of the receive array per ping interval (which in turn determines the range)".
I tried to search the Forum for the specs on the side-scan sonars used on Niku VI and VII without luck so I don't know how they compare to the Kongsberg UAVs. I did some analysis of Synthetic Aperture Radar (SAR) for a defense contractor years ago. The improvement of SAR over traditional search radar was remarkable. I'd expect quite a bit of improvement of Synthetic Aperture Sonar (SAS) over Side-Scan Sonar.
I've seen a number of posts recently that suggest expanding the search area. It wouldn't take much error in interpretation of the 'evidence' as a whole (Bevington object, eyewitness accounts, radio intercepts, etc.) to miss the actual location of the Electra. I haven't seen anything in the ROV videos that convinces me I'm looking at an airplane part. Considering the 'supporting evidence' (Noonan's experience as a navigator, bones, artifacts, etc.) I think the Electra is probably somewhere around Niku. I'd just hate to miss it with too tight a search area. I agree with other posts that the ideal case would be finding something on the island, or in an ROV video, that pinpoints the landing site with a high degree of confidence.