You are making this orders of magnitude more complicated than it needs to be. 10,000BC refers to a very rough number of years ago. Calendars are irrelevant. All you need to do is take the number of seconds in a year, multiply that by 10,000 and allow for change in year length.

I would suggest posting this on /r/theydidthemath for some more helpful answers here. It seems like you already have all the historic resources - you just need the mathematical help.

I don't understand what exactly it is you're asking, but maybe I can clarify a few points.

As others have said, historical calendar systems (e.g. Julian vs. Gregorian) aren't relevant. If we're talking about dates in the region of 10,000 BCE, they're really estimates of the the number of years that have elapsed since an event happened, rather than references to a fixed calendar system. So strictly speaking they are ages rather dates, although they are often expressed as dates for convenience.

The most common way very old dates are derived is through radiometric dating. Radiometric ages are given in years before present. The notation differs: archaeologists tend to go for the era BP ("Before Present"); geologists use ya ("years ago") or the SI unit a (and ka, Ma, Ga, etc.) But regardless of the notation "Present" is arbitrarily defined as 1950 CE. If you see a date before about 3000 BCE written as BC/BCE, it will have been originally a BP age that was converted by simply subtracting 1950 (or 2000, if it's a round number).

The "year" in years before present is a radiometric year, which approximates a calendar or astronomical year, but is not quite the same because of variation in the whatever underlying physical process was used to ascertain the age. The only context where this variation matters in radiocarbon dating, which is used for things that happened in the last 40,000 years. Variation in the ratio of ^(14)C to ^(12)C in the atmosphere means that the age of an event in radiocarbon years can be thousands of years out from its age in calendar years. Fortunately, we can use dendrochronology to account for this variation and convert ages in radiocarbon years to ages in calendar years. However, calibration is not exact and the calibrated value will depend on the choice of calibration curve.

One more thing to consider about radiometric dates is that they aren't exact; there's a measurement error introduced in the laboratory. For that reason uncalibrated radiometric ages are usually given as a mean plus the standard deviation, and calibrated ages are given as a probability distribution.

With with that in mind, what does 10,000 BCE actually refer to? Even if it were a single exactly dated event (say a piece of charcoal dated to that year), it would be an approximation of the number of calendar years that have elapsed since then, with a measurement error in the order of decades, plus additional (unquantifiable) uncertainty from the calibration. But if someone says that something happened in 10,000 BCE (like the start of the Holocene), they're more likely to be using a sort of informal estimate based on an average of multiple radiocarbon and relative dates, which means you're talking about a precision of ±500 years. Either way, trying to figure out the number of seconds that have elapsed since then is hopeless.

Because both "the Holocene" and "the Jomon period" are dated in this way, the Holocene Era and the Jomon Era can't really be considered independent calendar systems, more suggestions on how to modify existing calendar systems. In its original form, Emiliani simply proposed adding 10,000 to Gregorian AD years to get the Holocene year. You could use a more up-to-date epoch for the start of the Holocene―the current standard is 11.7 ka―but since that still has an error of ±99 years you still have to peg it to an existing calendrical system to reach an exact date and time.

I think what you need is the Julian date (as in astronomy). Since it increases continuously by days beginning from 4713 BC, you don't have to worry about leap days, calendar changes, etc. You can find a calculator on the web easily (e. g. https://www.aavso.org/jd-calculator).

It might help to invert your question. When someone says that something (the last ice age, an ancient artifact, whatever) is from 10,000 or 5,000 BC, what do they mean?

They mean that using carbon dating (for example) it's age has been estimated as such. Any estimation is associated with an uncertainty. For carbon dating this uncertainty can easily be on the order of 50 years (source: Wikipedia, I'm on mobile). So at this point your question becomes unanswerable. Or, perhaps better, the errors you are discussing are much smaller than the errors we have in attributing such dates to events.

I don't think you are going to end up with a satisfying answer. There are multiple issues here... namely because we have switched calendar systems so many times simply trying to achieve more accuracy. But, let's start with the most basic calendar. Time has never been exact, and has shifted. The rotation of Earth, it's orbit, etc... all of this is constantly changing, not to mention the fact that no day is an exact 24 hours. I have no idea how you plan to manage that. Our understand of time is just our own best guess of an imperfect system we try to measure. So... your problem is you just need to pick a way of measuring it and accept the imperfections. 10,000 BCE is just that. 12,017 Gregorian years (not exactly) before today, based on that calendar system. If you wanted to measuring it with the Hijri calendar, you would have to make adjustments because it is lunar, etc. You COULD add Gregorian years to Julian years at the moment of the switch, so on and so forth as you keep going back. But then there is the Hebrew calendar, the Japanese calendar, etc. Which one is measuring time most accurately? Or has been measuring time for longer? Eventually you will hit a point where there was no calendar, and then what? Which measurement will you use? When we say 10,000 BCE it is typically accepted as exactly that. You will not get an exact measurement for this, only a best guess, and the calculation for that best guess will be extremely subjective, and could have multiple different answers. Basically, pick a system and stick with it.