The usual model for option prices does not account for whether the underlying stock is cheap or expensive. The future stock price is assumed to be a Gaussian random variable, with implied volatility representing the normalized standard deviation.

I find a better interpretation is this:
The price of an option goes up and down mainly with the mood of the market.
The residual cost beyond theory (interest rate, time frame, moneyness factors) is given the name "implied volatility" to make it sound fancy.
It's named that because it's what the volatility would have to be if the theory were correct, which of course it isn't, and in any case the future volatility isn't known anyway.
Really it's just a measure of expensive or cheap!

It seems to me that when the stock is perceived to be expensive there will be relatively more call sellers, which will push the implied volatility down. (That's my intuition, not my observation).

One might expect this, but there doesn't seem to be any evidence for it as far as I know.
First, there is the theory of put/call equivalence, which means that the time premia for all options for a given underlying change in price at the same time.
The theory is imperfect, but reasonably close. Buyers of one are bullish, buyers of the other are bearish, but they both get expensive at the same time, so it's not the net bullishness that's determining the price.
More prosaically, the majority of options on prominent stocks are traded as part of some kind of combination. Go long the stock and simultaneously short using some option position, or a more complicated combination, sometimes covering a whole sector. So the buyers of calls (say) are not necessarily bullish on the stock anyway.
Lastly, high prices are seen as bullish to momentum players (and to be fair, not entirely without reason). There are probably more momentum players than there are people who have even a vague a handle on what the shares might actually be worth, so higher valuations might well be expected to lead to more demand for more expensive calls, not less.

Based on my necessarily anecdotal observations, the ratio of price to value does not seem to be something even considered by any meaningful fraction of the option trading community for any stock. It's not at all hard to find someone willing to pay you hard cash for the right to force you to buy for $0.75 something that is plainly worth $1.00.

Question is: how does that downward premium pressure compare to the effect of the overall option market volatility?

I suppose that any additional bid in any market will affect the price to some degree statistically, within the time window that trader joins the crowd. But it is probably not measurable except in extreme circumstances. The prices of all options tend to move together to a very large extent, so mostly it's the entire market you're trying to move with your trade.

The bigger and oft overlooked effect is that option trades can move the price of the underlying security, sometimes quite a bit.
An example:
If you write a call, there is a good chance that the counterparty is a market maker who sheds the risk by buying your call (a bullish move in isolation) and simultaneously shorting the stock (an offsetting bearish move), in a ratio based on the current option delta, to become neutral. As the stock price moves the delta changes, and the market maker will adjust the size of his short position to stay short term neutral. This is the main mechanism (in reverse) behind the Gamestop price spike.

Jim