I know you don't like it when I compare our OHLE with other countries, but this picture shows how over head can be made to be more stable at both speeds and in wind.
http://bienenstich.spdns.de/sites/default/files/pictures/1P7A6163.JPG
Note the Y wire between the top wire and the masts, that helps with stablilty, then the tiny cable from the mast to the contact wire holder, that helps with wind stability. It's called a wind protector. While this does not help with the issue of cross spans. (of which they were warned about at the time, We know what we are doing, came back the answer), it could help with upgrading the masts though windy places and be a quick (ish) fix.
The problem is oscillations of the contact wire resulting in the trailing pantograph in a two train coupled formation having such poor contact they suffer from VCB activation or worse, damage to the OLE occurs, it's a speed related issue and no amount of additional catenary wiring can truly deal with a contact wire than's not under sufficient tension for the job at hand.
HS1 has 22kN tension, compared with 12kN on the ECML (averages), 16.5kN average is the goal for GWML, MML and eventually ECML. The problem for the ECML, as I touched upon earlier, and which rules out wind protectors and additional catenary support is that the headspans can't reliably cope with the extra weight that comes from thicker, heavier contact wire and higher tensions.
There's certainly the possibility of using some of the foreign ideas for quick fixes to deal with wind deflection, but the general problem on the exposed sections of the northern ECML, which is most wind effected, is the idiotic 70m and 80m mast spacing on exposed routes, where 40m to 60m would be more appropriate, but that's because nobody wanted to wire Newcastle to Edinburgh initially, so masts were allocated against work on the southern end of the route and amazingly not used, work north of Newcastle was very cheap because there were so few materials needed. It's for the same reason Waverley is such a mess, and electrification round Edinburgh is so half baked.
Edinburgh to Newcastle, for example, really needs a dramatic increase in the numbers of masts per track km. It's probably making do with 12 to 14 masts per km when it really should have 20 to 24 per km, increase masts and you can increase contact wire weight and tension, which helps in windy conditions.