"Only" 115 mph

Considering the high performance "standard" rating was "S" (112 mph) for most tyres in 1969, I'd say "H" was darn good.
Tyre speed ratings relate to how well the tyre keeps its integrity (shape mostly) over a period of time at a given speed. Most tyres can easily go over their rated speed, just not for extended periods of time. These speed settings are established under controlled conditions, with application matched ideally for that tyre (i.e. best rim design and exact load).
Ply separation is much less unlikely to be the cause of tyre failure due to speed, and much more likely due to overload, underinflation, wrong size and bead separation. Ply bonds are put under stress by flexing. (such as from high speed elongation, but mostly from the factors I already mentioned), and ply separation happens when heat builds up to the point of weakening those bonds.
As speed increases, the shape of the tyre changes, growing taller and thinner. Tubes don't substantially alter this aspect, perhaps even shoring up a tyres resistance to changing shape, as long as the tyre and tube have been balanced together. Ply material and construction, sidewall and bead design, and compound are the major determinants of how well a tyre keeps its shape.
However, the rim is a limiting factor in speed rating and perhaps this is where the misconception that tubes reduce speed setting comes from.
Rims that require tubes, place additional rigidity requirements on a tyre in order for that tyre to be rated at higher speeds. In other words, a tyre that is able to keep its integrity on a tubeless rim, will break seal much earlier on a tubed rim - not because of the tube, but rather because of the rim and associated effects on a tyre's sidewall behaviour. Indeed, a tube helps the tyre retains its integrity, past the point where it would otherwise fail without a tube.
Since most tubeless tyres are tested on special tubeless rims, its a safe bet to say they are less capable when used on tubed rims.
If you want to keep those speed ratings accurate, you may of course change to tubeless rims. Or...use the Honda recommended tyre size, i.e match tyre width to rim and increase height/width aspect ratio, increase tyre pressure, reduce load, and get a really good tyre, tube and wheel balance.