Of the three options the addition of sulfuric acid might work the best. I live in an area with highly alkaline soils and can tell you that the addition of gypsum won't help much. I've successfully used microbes to treat various spills for customers and, as a microbiologist, like using bacteria as often as possible but for it to work in alkaline soils you'll need two things: (1) a source of sulfur (elemental sulfur or sulfide deposits) and (2) the most amazing luck keeping them alive if the soil is near the surface. Even using Acidothiobacillus spp. it would be very difficult without constant re-innoculation. Sulfate-poor areas in the US use diluted sulfuric acid with great success to significantly increase crop yields. Of course, everything depends on why the soil is so alkaline and if there is another source of sulfur available.
If you refere to Acidithiobacillus thiooxidans, it is quite complicated to keep it active at high pH values, due to it is an acidophilic sulfur-oxidising bacteria.
Graciana Willis is quite right about the bacteria not doing well at high pH values but your biggest question should be, "Where is the sulfur coming from?" If you control pH, shield the bacteria from direct sunlight and provide the necessary micronutrients they will still need a source of sulfur to produce sulfate. The simplest thing is to use sulfuric acid. (Growers in California US use a considerable amount of sulfuric acid in highly alkaline soils and it helps their crop yields significantly but there are other downstream environmental issues.) Unless sulfuric acid is really expensive it is usually the most economical source of sulfur.
Reducing salinity is difficult. Having lived close to the Great Salt Lake (Utah-US) that has occasionally flooded making large areas unsuitable for cultivation due to high salinity and pH I have seen three methods work for recovery of the land:
(1) If the soil is in an area that can be flooded with fresh water and drains to the sea (or inland salt lake) simply flood the land with fresh water (two floods with 6" of fresh water will remove 75-80% of the salt);
(2) There is a species of grass that grows on the outskirts of the salt flats that isn't merely halotolerant but actually takes up considerable amounts of salt. Some have grown as much of this plant as possible harvesting it (and removing the cuttings ASAP) to reduce salt concentrations over a several year period; and
(3) The most effective thing I've seen is using raised beds followed by irrigation using waters first higher in calcium then fresh water. This will help the soil in the raised beds fairly quickly with the least amount of fresh water..
Salinity reduction is not enough - you also have to increase the organic content of the soil once the salt concentration comes down. As this happens the pH of the soil usually goes down as a consequence.
I don't have any personal experience with strains that are any good at converting sulfur at high pH. (Most of the sulfur-reactive bacteria work best at low pH.) If you are wanting to try it your best option is a suspension of bacteria and nutrients from India called "Symbion-S" (http://www.tstanes.com/products-symbion-s.html). I'd like to know if it works (and how much it costs) if you try it. It would have to be VERY economical to be less expensive than sulfuric acid.
The acidophilic bacteria need specific conditions for growth. Usually they can grow at the acidic environment and increasing the Salinity affects their metabolism externally. Although you can adapt you microorganisms to the new environment, my experiences show that they cannot grow at conditions that you mentioned (pH more than 7.5 and EC: 5000 - 15000)