IMO this will matter only if we are allowed multiple listings, there is an atmosphere to enter the thread, discuss, comment (as in the old B&S). Otherwise I'm just going to click and then 'get out'.
I prefer the old price drop method or a combo of price drop and payment to SF. If all the seller needs to do to bump is pay SF for it, then they may not feel the need to drop prices, which was IMO a crucial part of the old B&S and important to buyers. Apart from the deals and the community aspect of the old SF, the 'hold your nerve until seller drops prices' was both exciting and good for buyers. So I am against any system that does not encourage sellers to drop prices.
This is good for sellers as well. In the end, 'good' deals were the key drivers of sales; AFAIK, few sellers actually sold everything until they dropped prices a few times. Under the system you propose, sellers may find they are both paying SF to bump, and dropping prices. The bump will not by itself improve chances of a sale, a price drop will
My eye goes there first, but it then is the first thread I dismiss if it is not relevant to me. So I'm neutral/ indifferent to this.
I don't yet have an opinion on other questions because I have not tried it (Search) or feel they are not relevant to me (Power Seller).