If photosynthesis affects the pH to any significant degree, then my tanks are going to be all over the place, because they are all at least planted to 75% substrate coverage. I know this is not the case, as the only pH drop my tank experiences is 0.4 at night when the CO2 degasses. I no longer ever test my tanks unless I feel something is wrong, but I did monitor them in the early days to learn what is happening in there. Your algae is not affecting your pH to any worthwhile amount.
For algae to bloom, it needs a germination trigger. Some people will blame your algae on phosphates levels, and others will blame it on nitrates. These are both nutrients used by algae, but they do not trigger it. I actively add nitrates and phosphates to my planted tanks, but have never triggered algae in this way. I even increased the nitrate level in a healthy growing planted tank from my usual 20ppm to >50ppm for a protracted period with no increased plant growth and no algal bloom. I have also grown algae in a glass full of RO water, simply by adding sunlight, so depriving algae of nutrients will be nigh on impossible. So, if your tank is not receiving direct sunlight, it is unlikely that light is the cause, although it would be useful to know your light levels and photoperiod.
For your plants to have algae growing on them, then they must be unhealthy. I am not sure what you mean by medium stocked with plants, but if you have around a 50% coverage of plants, then having air bubbles is going to degass your water of CO2. The carbon from CO2 is essential to the photosynthesis of your plants, so if it is in short supply, your plants detect this and they start to produce RuBisCo to fix carbon. This requires a lot of energy from your plants, meaning that their growth is slowed down and deficiencies start to appear. If the deficiency is carbon, your plants will start to suffer quite quickly.
As a consequence, unhealthy plants leach ammonia. Ammonia is another good way of triggering algae in my experience, so with a constant supply of ammonia around your plants leafs algae will bloom.
Light levels are the major factor influencing growth rates in your tank, followed by avaialability of carbon. If your light levels are sufficiently low, then they won`t be driving a large nutrient uptake, so your tap water may well contain enough nitrates and phosphates to support the slower growth. You may want to consider adding trace elements via a reputable source such as Tropica Plant Nutrition.
My advice to you is to get rid of the air bubbles, keep cutting off the algae affected parts of the plants (plants love pruning), improve CO2 levels and add trace elements. I would also give up disturbing the substrate as well, if I were you, as this releases ammonia in to the water column and triggers algae. I have never vacuumed any of my tanks at any point and have never seen the point in a planted tank.
In summary, I think you need better CO2, better trace elements and to keep hassling the algae.
What would be interesting is a picture of the algae to see what type it is and how advanced it is, a list of the plant types you have, and your light levels and type.
Dave.