I see two possible solutions for the players, and two for the GM. I’ll cover all of them here.
For the players: Track value only at transaction time.
In other words, track exactly two things:
- Total amount of each currency the party has, as an exact single number (or set for P/G/S/C pieces).
- Known relations between factions. A simple table is probably easiest here.
Then, when they actually want to buy something, they just use the table of faction relations to pick what currency to use, and treat it as a ‘normal’ transaction from a typical perspective.
This greatly simplifies things for the players while still keeping the aspect of economic fallout from wars that you state you want in the comments. It can also be simplified even further by the players just asking the merchant they are buying from what currencies they accept at what rates, thus eliminating the need for the players to track faction relations.
For the players: Carry wealth in non-monetary highly liquid assets.
Essentially, when selling things, instead of asking for money they ask for the equivalent value trade goods, gems, or similar things. Choice of what they’re using here is going to have to vary by where they expect to be buying things (small villages will probably not care about gems or things like platinum or saffron for example), but should not be too difficult.
From there, they either exchange these assets as needed for local currency, or barter directly when possible (for example, the inn they’re staying at may actually be happy to accept payment in the form of rare spices).
Depending on how this is handled, it can either be much simpler than what the party is doing now, or it could be much more complex. However, it inverts things so that the problem becomes one the GM has to deal with (because this completely sidesteps your goals of making wars have an economic impact unless you take an absurd amount of time to make a full economic tracking system)
For the GM: Throw out this system, and have wars impact availability of goods.
In other words, instead of adjusting effective value of currency based on faction relations, adjust what can be bought based on the overall state of diplomatic relations in the region and whether the party are allies or not.
If the party are known to be hostile to a given nation, and that nation is at war, said party probably will have difficulty purchasing anything in that nation.
Similarly, if the party are neither allies nor hostile, they may have trouble procuring weapons, armor, and healing potions in a nation that’s at war (because production of those items will likely be directed solely towards national defense), but may not have significant issues procuring more mundane things like regular clothing or trade goods.
In essence, instead of manipulating exchange rates (which essentially never happened IRL in pre-modern times to the degree you’re using), manipulate market availability directly (because that was an issue historically, and actually had a far bigger impact than the value of currency X in nation Y).
For the GM: Throw out this system, and instead make diplomatic relations have tangible RP implications for the players.
This is the approach I would actually take to achieve your goal in D&D 5e. The reality is that 5e, RAW, has essentially nothing for players to do with gold once they get their full non-magical kit set up other than buy healing potions, and possibly components for high-level spells. IOW, unless you have some other important gold sink you’ve created in your setting, high level players will be (mostly) unaffected by the system you describe.
Instead, if you want to make wars feel impactful, actually play out the diplomatic issues resulting from them. As a trivial example, if two nations who share a border are at war, then crossing that border becomes extremely dangerous and difficult (possibly even impossible depending on tech levels). That, by itself, can have a huge impact on the party because at minimum it increases travel time, and at worst may make it borderline impossible for them to get into a given nation for a while.
Similarly, if the party are known to be allied with a particular nation, then they will effectively have to deal directly with the fallout of diplomatic issues between that nation and other nations when trying to deal with the government in those other nations.
These kinds of issues will still impact even high level parties, albeit in different ways from how they impact low-level parties (sure, you can use a Gate to get around the border closure, but if it’s discovered it will probably be an international incident), allow more granular control on the part of the GM, and only require extra effort from the players when they actually encounter such issues (instead of imposing a constant overhead on them all the time).