Honestly, I think you’re doing pretty well with what you have. A few pointers:
Your run up and shields
I’d pretty much do as you’re doing. You need to be aware of what your equilibrium point is with your current roster, which is the point at which you can stay unshielded, and lose few, if any points. Your equilibrium point is likely to vary a little from week to week, depending on the boosted character, and whether you can field a featured character who’s any use to you at all. If you really want to conserve HP, play to your equilibrium point, then run up as high as you can when you’re ready to push. I wouldn’t really advocate shield hopping at your stage, it’s a fairly extravagant spend of HP to do that for a 3* cover.
You need to pick your time to push. Be aware that people will tend to push at -8 hours and -3 hours from the end of any event, so they can use shields at that point. Times in between that tend to be quieter, so you’ll tend to take less retaliations, and fewer incoming hits. If you really want a cover, you could try pushing at 5-6 hours out from the end of an event, and use an 8 hour shield to finish. Otherwise, pushing at around the 2 hour mark from the end of an event is probably a reasonable strategy. Pushing high in the last half hour with a 2* roster in the higher point values is likely to turn you into mincemeat.
Time slices
Time slices do matter. Some slices are more hotly contested than others. A score that will get you T100 in one slice, won’t cut it in another. Slices 4 and 5 tend to be high scoring, the others less so.
Picking your point values
Make sure that every target you hit is worth a substantial number of points. The bigger the better. This is for two reasons. Obviously, firstly, it makes your run up more efficient. Secondly, it means that your retaliation value (at least at the point of the match) may not make it worth it for them to hit you back. So, if you hit someone for 60 points, and you’re only worth 20 points on the retal, they’re more likely to skip the retal. If they’re silly enough to hit you for the retal, hit them again. Every retal is a net positive gain for you. As a rough guide, with the new point scoring method, I prefer targets around 50ish+, and I generally won’t hit a target worth less than 40 points. Definitely don’t hit any targets worth less than 38 points.
Likewise, try not to hit low point value targets, as your net loss on the retaliation won’t make it worth it. The only exception to this is if their team is so inferior to you as to not be able to retaliate successfully. (Beware of the sucker punch, where a strong player will deliberately field a weaker team, in the hopes of farming large point value retaliations.)
Use that skip button liberally.
Pick your events
Finally, obviously, pick your events carefully. You only have a limited number of HP, so you don’t want to spend HP shielding for a cover you’re not going to use in the short term anyway. The aim is to pick up enough covers in top tier PVP characters, so you can make them viable, which will, in turn, make placing T100 easier, and easier.