First off, that pair of wealth rules looks good. They'll work, and you're not going to break your game by using them. Go for it.
Wealth in tremulus is a straight port of the wealth rules in Apocalypse World. In AW's system and context, jingle, it's lack, and its ease of losing are part and parcel of the scarcity theme that pervades the game and the post-apocalyptic genre generally, and the AW wealth mechanics play nice with our genre expectations. In tremulus, which is set in the (relatively) modern day and the context of a modern banking society, the wealth rules still work fine but they jar with our personal, intimate familiarity with our monetary system.
There's nothing wrong with the rules, except that we know too much about what they model for our suspension of disbelief to be easy. It's like a war veteran playing a very game-y wargame: they might easily be distracted and annoyed by the parts of the rules that, though they work just fine in the system, don't match (or worse, disagree with) their own experience.
So I get where you're coming from. If you want to use the rules as written, here are a few things to keep in mind as mantras or touchstones to buttress your suspension of disbelief:
1 Wealth all by its lonesome is not the same as 1 Wealth that has company
The abstraction represents, in part, the adage that it takes money to make money. When you've got 1 Wealth, you don't have much in assets or leverage. You can't do much with it except get by. But add 1 Wealth to that and you go up a whole rung. That abstract 1 doesn't mean you got another handful of bills that matched the other, it means you hit an inflection point in your buying power: you already had the necessities covered, but now you've got enough to lift your finances to a higher level. You've got capital to invest and make yourself some more money. That's why 3 Wealth can buy you a car, but 1 Wealth and 1 Wealth and 1 Wealth held by three different characters doesn't add up to a car's worth of fictional bills in their wallets.
Spending Wealth is losing narratively-relevant liquidity, not losing a twenny
When you've got 3 Wealth and you pay a cheap bribe, you lose nothing – except when it's relevant to the story. A bribe that means nothing to the story and your achievement as a PC doesn't cost 1 Wealth, it costs a few fictional bills that you can afford to spare without worrying about it. You can just do that, and the system doesn't engage. But when you're trying to achieve something, then the system engages and says "This is an important spend. You can do this, or you can keep your ability to buy that car. Which is more important to you?"
Cost-1 is not an absolute amount of money, it's an implicit question about how much you want this spend to change the game. If you want the change, then this spend just so happens to be the time that you hand over those bills and then realise that it's the straw that broke the camel's back. It pushed you over an inflection point in your finances, and now you're dealing with higher credit fees, overdraft fines, moving your investments out of long-term deposit to cover living expenses, or some other snowball effect that's going to hurt your ability to afford those big-ticket items. But we aren't playing Bankers & Balances, so we don't care about the details and just abstract it.
The ability to buy a car doesn't matter unless it matters
When you've got 3 Wealth and you bribe a (narratively-important) clerk, you go down to 2 Wealth, sure. Now you can't buy a half-decent car. Did you want to buy a car? If not, then it doesn't matter that you can't anymore. Thinking about not being able to afford the car that you didn't even want to buy is just a distraction, and irrelevant to the game you're playing. You only lose the ability to buy that car if you wanted to buy that car.
If you're playing a game of skulking in dive bars, abandoned farmhouses full of cultists, and getting lost in the moors, and you're never going to use Wealth for buying cars, fancy clothes, or chartering a ship, then you're not losing those things. In that game, 3 Wealth won't be buying you a car, so it's fine if it's all gone after bribing a clerk, buying a gun, and spending the last of it on an interstate taxi ride. It's probably a one-way trip anyway, isn't it?
But like I said, we're not playing Bankers & Balances, so we don't care. We just want an abstraction that works so we can get on with the game. The Wealth rules as-is work well enough, and so do your house rules. Whichever results in a game that is more about creeping insanity and less about fighting to maintain your suspension of disbelief, do that.