I think you got the total 230 ton thrust for 116s for JAXA's SRB-A3 wrong. It should be approximate 160 ton thrust.
Here is the link to JAXA (and I used google translate) http://www.rocket.jaxa.jp/engine/srba/
The long term combustion motor (116s burn) has a 76.6 ton overall mass with propellant mass of 66 tons. Specific thrust is 283.6 seconds. That sounds right.
Now if you want to design a new rocket, with a goal on improving either cost or efficiency or both, you have actually very few options.
Let's agree to the following, in general:
1. SRBs are low cost and are low efficiency compared to Cryo-engines which are high cost and high efficiency. Hypergolic motors come in between.
2. Fabrication cost of a stage significantly outweigh the propellant cost. In fact the propellant cost is miniscule compared to engine and stage fabrication.
3. An all-up integrated rocket cost is not determined just by the sum total of its engine costs, but it is determined by its "integration cost". Integration cost among other things also includes the turn around time of the launch campaign. The Delta-IV Heavy has a launch history every 1.5 years which is now attempted to be shortened to every year. This enables fabrication costs to be lowered. In fact Arianne 6 is now redesigned to be same capability as Arianne 5 but with lower fabrication and integration (or launch) costs. https://spaceflightnow.com/news/n1403/27ariane6/#.U2v3InLSW-M
4. Cost of an unreliable launcher far far exceeds the the cost of a reliable launcher, even though the later might be both inefficient (say all solid) and costly.
In effect, you have different matrices for both cost and efficiency. And then you have mission goals.
Given the above, let's see where your designs fit in. Let's take:
Design I-3 -> GSLV MkII with 4 S60s instead of the LH40s. Delay the ignition of the core to T0 +50 seconds.
Reason: Config 3 will have almost same payload as GSLV Mk2, except it will cost less.
Your proposal is to replace the 4-LH40s with 4-S60s to save on the cost. However one of the GSLV-MkII stated goal is to delay the first stage ignition until the LH40s develop the required thrust on ignition. In effect you have violated the stated first goal. Further you have introduced a variable of air-igniting the S-139 . ISRO's record on air-igniting large solid core stages is patchy (see ASLV) and the only air-ignited solid stage ISRO has is HPS-3 (PSLV 3rd stage).
An alternative will be to just replace the S-139 of GSLV-MkII with S-200 of GSLV-Mk III. An interstage that goes from 3.2 mtrs to 2.8 mtrs will suffice to stack the second and third stage. This is not a major design change and a single live test will suffice to confirm the aerodynamic loadings. It can use it on SSLV itself as a test bed. The burn time of S-200 is 128 seconds compared to 100 seconds of S-139. In fact, the S-200 can have a little longer burn time, a 20% slower burn time will align the burns appropriately. Ideally if the propellant loading is increased to 240 tons, (S-240) if you may, its SI will be similar to JAXA's SRB-A3 except approximately 4 times larger and burn time aligned with the LH40s. This will take care of the stated "inefficiency" in GSLV-MkII.
Either way, the alternative suggested is to achieve a commonality on the SRB. If ISRO can standardize on S-200 (or S-2x) series, it can go for automated fabrication of S-200. The S-200 can also be the booster for the SSLV.
With a standardized solid booster for SSLV (small sat), GSLV-Mk II (medium lift Polar and GTO) and GSLV Mk-III (Heavy-lift)., ISRO can now achieve a common fabrication and reduce costs considerably. Also ISRO will require a large reliable booster for its TSTO-RLV and will require a medium lift vehicle (Mk-II) for space sciences (chandrayaans and mangalyaans).
Options to redesign GSLV-MKIIIs and skew its payloads towards medium lift category) are a no-go since that space is already occupied by GSLV-MkII. In fact GSLV-MK III should evolve into a heavy lift vehicle like Arianne V, and with commonality in reliable stages across its small, medium, heavy and reusable launch vehicle families the cost to access the space will come down drastically. At this point, raw stage efficiency does not matter.
A cheaper, faster and reliable access to space beats a "stage efficient, but costly, slower and unreliable access" to space any time.