Here is the latest plan for achieving a Diplo victory. Let me know if anything is missing. (I know it's a bit light on Pop and diplo relations but we are trading with everyone and just need the techs at the moment).
Research
Electricity > Radio > Mass Media
Electricity due in 9 @ 70%
We failed to generate any Great Scientists in the last turnset as changing to the GP spamming civics of Caste System & Pacifism ended up being incompatible with maximising the research rate. Gandhi beat us to Physics by a mere 2 turns and so we ended up with no Great Scientists to set towards Physics or Electricity. With 20-20 hindsight we should have maximised research earlier.
Moving forward we are still in a good position to use some Great Artists to help research Radio & Mass Media. Li Po is sitting in Susa under orders not to culture bomb the city as the culture situation on the Indian border seems to be improving as our capital is now Pasardadae. (The % Indian population and chances of revolt in Gordium, Susa and Bactra still need to be watched).
Moscow is building slowly towards another Great Artist and has something like a 95% chance of generating one. This will need to be speeded up eventually but nothing needs to happen for the next 20 turns except running Artists in the Theatre.
We have a Great engineer that can be moved to Persepolis to eventually build the UN there.
Key Economic Stats
Treasury 2xx +9/Turn @ %30%
Unit Cost 28 (this should be <10)
Unit Supply OK (0 gold, I think)
Military - Size & Disposition
The unit maintenance cost is too high, I recommend you try to reduce this over your turnset to single figures. If I were playing I would disband virtually all axes/swords and most of the chariots while keeping the more useful ones as mps.
My preference for which obsolete units to keep would be 1) any that can be promoted right now to medics 2) any with lots of experience that we might want to upgrade to modern units in an emergency (~14XP or greater) and 3) chariots as they have greater mobility and so make more flexible mps than axes/swords.
This may mean moving some units around before disbanding to maintain enough MPs where needed while making sure the least experienced chaps are the ones disbanded. I'm sure you can manage this.
At this stage I would keep our maces, pikes and knights and rearrange them as mps where necessary and to meet the HC threat. The ones in Persia should mostly be ones with defence promotions.
This will allow us to afford to build riflemen in our Heroic Epic city of Elephantine.
As part of the redeployment we should not actuall disband our galleys. Some should remain at Tarsus/Sidon crossing. The remainder should generally towards HC. In particular I woul dlike to see 2 suicide galleys on each of our water resources off Giza and anywhere else under threat. If HC attacks with a single galleon he will be unable to pillage the workboats like he did just recently. We can have our own galleon in reserve to attack his wounded galleon.
Part A - Important Points
1. HC is not bothering us too much just some naval action. Check our fleet is screening him properly and build more galleons if needed. We can't afford to invade him at the moment or our economy will suffer again.
2. We are running civics which are good for science.
Free Religion
Free Market
Free Speech
There seems little reason to alter these.
We are still in Hereditary Rule as we have not got anything better.
We are in slavery and can whip whatever we like at Persepolis. However, you can freely swap to Serfdom if worker action is needed.
3.
Unfortunately the cities are still not optimised. There is too great an emphasis on hammers in places that are building research which is stagnating growth for no reason - see Part B for specifics I have noticed.
4. FDR is willing to give us
Rifling or Nationalism, 60g and WM for Physics. We should take Rifling sometime soon.
5. We can renegotiate our fish for 6gpt deal with Sally for 7gpt
6. We can renegotiate our rice deal with Gandhi from 11gpt to 12gpt.
7. Susa is up to 21% Egyptian and the chance of revolt has dropped to a mere 0.9%.

The tile 1E is down to 63% Indian and wil soon flip to us. Report on this.
8. Gordium has dropped to 71% Egyption but there no chance of a revolt at the moment. Maybe we should whip the temple there for 1 pop (Due in 33 by build alone which is far too long).
9. Our borders in Persepolis have expanded so there are 2 forests we can chop 3 tiles to the S of Susa. This will greatly help build the culture improvements there. One is 3S of Susa the other 2S1SW. We should get some workers to the one 2S1SW urgently and chop it just in case Gandhi's culture takes it back.
10. We have a mad worker called Rosicky who has build a useless farm between Elephantine & Heliopolis while we actually need one 2NE1E to irrigate the rice paddy. Please get this to happen.
11. I think we can now build lumbermills in our forests. Any forest being worked should obviously have one as a matter of urgency.
Part B - Micromanagement (MM)
# Persepolis govenor is on for food. This is OK but commerce should also be selected.
# Thebes, Memphis and Heliopolis have stagnated, I think it would be better to have them growing a bit by moving citizen off plains hills onto water tiles to access a little more food. The water tiles each produce 2 commerce so there will be little impact on research.
# Moscow is almost ready to grow but has no surplus food. A bit of MM here will really help. It could work the uranium hill which will be better than leaving that to Sidon as Moscow has more commercial and science buildings than Sidon.
# Elephantine can be MM for more food and commerce and still build Observatory in 8
# There is a village worth 4cpt at pasardadae that is not being worked and one of those annoying AI placed engineers in its place.
AAAAARRRRRGGGHHHH