Q:

How to implement micro periodization in a routine covering a wide rep spectrum

I wanted to train for strength, with no hurry.  Forced by the personal need of building strong conective tissue and avoid injury at all costs (42 yr, untrained, somehow prone to injury) I implemented the following strategy for each exercise: I use a fixed load and increase the volume by adding reps, from 3 sets of 3 reps (in the strength range, no doubt) all the way up to 3 sets of 15 reps with the same load. 
It takes a lot of training sessions to reach 3x15, because each workout I never add more than 3 reps in total (one per set) as a rule, and very often I only add 1 rep.  By the time I reach 3x15, it feels safe and sometimes even easy to increase the load (and start again the cycle with 3x3) so there is no doubt my strength has increased. 
But lately the volume seems too much, I need too much time to recover, and another answer to another question here has suggested I might need some kind of micro periodization, which I think it is the right way.  Also, I think I could try also to reduce the overall volume when close to 15 reps per set (e.g. by switching to 2 sets after having achieved 3x12 or somehing). 
How can I implement that periodization in a simple way?  For instance, after achieving 3x10 I could start alternating the high rep workouts with the next level of resistance and low reps.  E.g. 40kg x 3 x 10, the next workout 45 kg x 3 x 3, then back to 40 kg x 3 x (10~11) and so on. 
As much as I would like it, 5/3/1 is out of the menu because I can't train all the time in such short rep range, it is not for my age and fitness level. 

A:

The principles behind 5/3/1 are still pretty sound, although the rep ranges aren't the best for everyone. 
Here's the good:

It's an example of micro-periodization over a month
** High(ish) reps, Medium reps, Low reps
Average work load for the month is between 75-85%

My coach had me do something 5/3/1 like for a while and it worked well for me.   It was more of a 10/8/5/3 plan, but I can take some principles from that plan and apply it to you:

You need to train hard every session, but still recover
Each Training in your micro-periodization should have a goal
Common goals include:

Volume: this is where strength is actually built
Heavy: this is where strength is tested
Speed: this is active recovery that helps with reinforcing movement patterns
Bodybuilding: more focus on accessory and isolation movements, i.e. fixing weak areas

Build your monthly pattern after these training styles

The plan you've been working with is basically a volume progression, which does work.   Doug Hepburn built a career doing something like that (but with heavier weights and lower rep ranges).   However, by not doing any heavy work, your body is acclimated to the way things are going.   Heavy work in turn also burns you out more quickly, so it has to be balanced out by allowing a bit more recovery. 
5/3/1 accomplishes this by having you work with high(er) reps and working progressively towards fewer but heavier reps, then gives you a week for active recovery.   While a number of people thrive off of this pattern, it's not the only one that works. 
Shaping your goals:

You should have a target number of reps per training goal

Volume: aim for 24-32 reps total for the week, with 8-12 rep sets
Heavy: aim for 8-12 reps total for the week, with 2-5 rep sets
Speed: aim for 8-15 reps total for the week, 1-3 rep sets
Bodybuilding: chase the pump with as many reps as necessary

You should have a target weight per training goal

Volume: aim for as heavy as you can for those 8-12 rep sets, feel free to remove weight each set
Heavy: aim for as heavy as you can for those 2-5 rep sets
Speed: aim for a weight that is slightly above warmup (roughly 65% of your current max)
Bodybuilding: go with something that will help you feel the muscle you are trying to control

Now you can decide how best to put all these together.   I've seen some programs have you mix it up so each major movement is done each week, but each one has a different goal during the week.   I've seen some programs where everything is on the same goal each week.   Your approach should fit you best.   That said, here are some common approaches:

Linear Periodization: everything moves in the same direction.   For example from light to heavy or heavy to light. 
Undulating Periodization: The weights are going up and down from week to week.   Kind of like a progression where each week you are doing sets of 10, 5, 8, then 3.   It's lighter, heavy, light, heavier
Mixed Periodization: each main movement has it's own progression, but all the movements are using different focuses each week (Brandon Lilly's program is like this). 

The training goals I listed are not the only things you can pursue, but just provide a starting point for conversation purposes.   The main take away is that you do need some heavier work than you have been doing, but after heavy work you need some recovery. 
Hopefully this is enough to get you working on your own plan.