There's nothing wrong with HIT, you just need to understand it and where it strikes it's balance. Once you know that, you know when and why it may or may not be appropriate to use. Certainly it can be very useful at certain periods. This is about progression and whatever training one chooses is simply the methodology for how they intend to go about getting it (and there should be some quantification of progress i.e. your X rep max in a big lift that you hold as a constant benchmark all year to evaluate real progress vs. acclimating oneself to just different stimuli or training). Once people expand their understanding of training theory, they are quick to realize that there is no golden mix of variables and single perfect scheme but optimally the scheme and variables will change over time as the trainee evolves or be deliberately changed to manage fatigue from higher workloads employed (i.e. more workload over a period = more stimulus even if it's dogmatically adhereing to one set and just increasing the frequency and then decreasing it as the sole method of manipulation).
So what people are promoting is training theory - the various 5x5 templates were just tools to explain it and give people an easy to follow and good experience with it. No one ever laid a 5x5 program in stone and called it perfect. It's a hypothetical snapshot in time. What people don't like about HIT has nothing to do with HIT and everything to do with the idea of a perfect program and that the optimal ways of going about something are to dogmatically keep everything static no matter what. That and the fact that some of the more vocal people adhere to it like a religion and don't have any understanding of the fundementals behind it. That specific range of variables most associate with HIT is not inherently bad and is valuable to employ; progression using repeated effort to failure is also valuable at time (you see this at the end of a SF 5x5 when it begins to stall), you also see it during a heavy loading phase where performance will dip and failure will occur.
Progression is the goal, all reasonable programs and mixes of variables can work at one time or another. What I advocate is broadening one's understanding to see why. But obviously BBing is a thing born of attachment so people tend to get caught up in whatever is working for them so I have to say this once a month or so just to reclarify the position. If someone likes HIT, wants to try it, or has used it successfully before, I have generally made the recommendation that they run something similar using moderate rep ranges after a higher volume program and see how it works (actually this should be the ideal time to run it as the neural gains will allow strong progression over a period through higher rep ranges and training to failure could be a decent way to scale it). I've said this to multiple people including Go2failure (who really loved and had fabulous results from the periodized program - you can search for his journal) as well as several others.
I'd probably advise not a complete rest for 10 days. Use light weights, lower volume, work on speed, doesn't matter but complete rest for that kind of period is generally only optimal if one is heavily overtrained and breaking down or just needs a mental break or vacation.
My inclination would be to shoot for something using higher reps for a period since you just peaked out in triples. HST has this implicitly. HIT is fairly easy to set up and tends to higher reps - a HIT flavor with a twist of speed work and slightly higher volume is Bio-Force's Direct Compensation Training, I've spoken with him at some length and while I don't believe in golden programs or that the specific mix he uses is going to be optimal to hold constant for long periods with advanced trainees, it certainly can work for people and makes more sense than most other flavors for someone who can handle a periodized 5x5 program. You could always take what you've learned and put something together yourself that you feel addresses your goals - people would be glad to look it over. You could try DC training. You could do DFHT is you tolerated the workload from the periodized program well. Even Korte or WSB if you want to further your absolute strength in the big lifts. Pretty much a blank page and that's a nice thing.