If you want big Olympic lifts, then there is only really one option.
You also need to learn how to snatch, as what you learn from that will improve your clean, too.
I would ditch your snatch grip stuff as it won't really help your Olympic work, and just focus on more Olympic lifting: if you think about it, you'll be getting a similar-ish stimulus to deadlifts and squats with each snatch/clean, so...
Regarding your ability to power clean more weight than you can actually clean, this is precisely how I started. It's pretty cool, you feel like a legend and everybody in the gym think you're a beast. However, I have just spent the past four months re-learning the lifts to improve the deep catches, as this will be key to increasing the lifts in the long term, and it is what you will have to do when it comes down to getting meaningful increases. As such, my clean 1RM record hasn't increased in nine months, but my technique is now a much better foundation for any progress I decide to make when I finally get a couple of weeks' consistent training in.
As a result, this is where the 70kgs number came out. I'd probably try it at around 60kg first to see how you get on, and literally pull hang clean after hang clean (or full clean/whatever) and - even though you won't have to - sit deep and catch deep. Once you've nailed this at 60kg, increase the weight by 5kg and keep going until you stall again. Then back off 5/10kg and keep going. for a week or so at that weight.
This is one of the things with Olympic lifting: you will probably need hundreds of reps to get the catch right to the point where you will know it feels right. For instance, two weeks ago, I upped the weight and wound up catching on my toes which isn't good. Two days later, with more work, I'd addressed the problem (I'm lucky as I can train at home). This takes a big number of reps, a lot of well-managed food, and even more sleep.
Take a video of what you're doing, too, if you're unsure. I'm curious as to how you feel the second pull let you down and how that translated into not getting under the bar fast enough. I think I know, but will leave it to you to furnish me/us with the requisite information.
And learn to snatch. It is actually much easier than the clean.
If you've got three days (with your current program considered):
MONDAY 3 rep sets (number depends on how much time you have)
- Power clean to push press (get you warmed up)... 3 sets, at a guess.
- Full clean (or I do full clean -> 2 hang cleans) and jerk;
- Front squats (heavy)... 4*3
WEDNESDAY Beach day...
- Back squats (heavy, 4*5);
- Bent-over rows (5/6 rep sets);
- Bench'
- Chins/whatever...
FRIDAY same as Monday.
Spend most of youre time on the full clean during the routine as this is where you want to be strong. Power cleans will get the juices flowing, as the full clean will get you in the positions you want and make you really work hard for those kg.
Back squats (high bar) are important assistance for snatch work, so get them in there, too.
You need to learn to snatch. End of. Once you start work on it, simply add it in before you clean work (if you have time). We'll cover that when we get there.
I would also be inclined to ditch your current Wednesday mobility thing and do it yourself in your spare time.
Regarding loading, depending on how crap you want to feel each morning, keep your working rate at around 85% max: if you go in straight at any more than that, you will really hurt a lot. Slowly build on your work rate, so you will do two days of 85% max lifting (Monday/Friday) and Wednesday as a rest day (as such). As your body adapts, you can ramp the work rate in terms of days training, as well as the loading pattern.
The Western way of loading that I've seen is pyramid-ing the weight (i.e. 5 triples at 60%, 3 triples at 75%, 2 doubles at 85%, two singles at 95%). This helps you build up easily and then go for some big numbers right at the end.
The old Eastern Bloc method of training is to train heavy, every session, every week. With at least 80% on the bar... this goes for all their lifts. This will kick your proverbial, very, very hard if you go for more than twice a week, but you might want to try it out. If so, start light.
Either way, you will have to disengage your brain from the idea that big squat = big Olympic lift. It does not. View them as assistance exercises, only.