Can I go to the UK, Ireland, or maybe Russia or Ukraine for a few months to reset my Schengen limit?

You apparently haven't understood the actual 90/180 rule. The rule states that you must not have been in the Schengen Area more than 90 days in any 180 day period.

So, on any day, you need to check that in the previous 180 days, you were not more than 90 days in the Schengen Area.

The 180 day period doesn't "start" anywhere, and can't be "reset", it's just a rolling period.

If some of your 90 days in Schengen were 180 days ago, then they will "slide off" the 180-period with time, allowing you to remain in the area, as long as you do not exceed 90 days out of the last 180 days at any time.

For instance, you had arrived in the Schengen Area on September 1st, and stayed for 30 days, then came back 90 days later, then stayed 60 more days, you would be in the Schengen Area for 90 (30+60) days out of 180, which is fine.

The 181st day, your "first" day in Schengen would no longer be counted (you would count from September 2nd), so you could still remain in the Schengen Area. And so long for 30 days.

On the 210th day, you would have stayed 90 days out of the last 180, still fine.

On the 211th day, however, the day that slides off (the 31st) would not be a previous in-Schengen day, so you would get to 91 days out of the last 180, not fine.

So, without a detailed travel history, we can't tell you how much longer you can stay or not.

In any case, you cannot stay more than 90 consecutive days, as this would automatically break the 90/180 rule.

Again, exiting the Schengen Area does not reset the count in any way, you just stop accruing days-in-Schengen, but those won't reduce until they "slide out" of the 180-day window.

Note that any day you are in the Schengen area, even if just for 5 minutes, counts for a full day.

Also note that you should not plan to skirt as close as possible to the limit. Stuff happens, and you could overstay because of all kinds of issues (delays, cancellations, weather, illness...). Always keep a margin of a few days.

Note as well that the rules in some countries (including Poland, I believe) are slightly different for citizens of some specific countries which had previous bilateral agreements. You should tell us your citizenship if you want more details.

Finally, remember that on a standard visitor visa, you are not allowed to work. Staying as close as possible tot he limit may be an indication that something is going on which may be a problem for future visits.

Edit given US citizenship

In addition to the general 90/180 rule, there are lots of special cases. Relevant in your case, per Wikipedia:

Above the framework of the Schengen visa exemption of 90 days in any 180-day period, Israeli, South Korean and United States nationals are permitted to spend an extra period of 90 days visa-free in Poland

The reference used is this document, page 43, which states:

It is also important to mention the specific situation of some of third country citizens, who are not subject of the visa requirements. They are not obliged to obey the limit of stay to 90 days in every 180 days without visa. Bilateral agreements between some of the third countries and one of the Member States foresee the possibilities of stays to 90 days without any additional requirements. European Commission, on the basis of Article 20 point 2 Schengen Convention, expressed the opinion, that people, who are subject to those agreements, can leave the country after 90 days and the next day they can come back to the country, starting the new 90 day period. They are not obliged to leave the Schengen zone, if the country of origins signed this kind of bilateral agreement with more than one Member States. The cases concern inter alia the citizens of USA, Israel and the South Korea. So those people are able to stay in the Schengen area for longer time in the conditions of the short stay without the visa requirements.

(from what I gather, the only other Schengen State the US has such a bilateral agreement with is Denmark, so you could either go to Denmark and back, or exit the Schengen Area and come back).

I would however personally try to get further confirmation of this before attempting it, just to be sure. Even though this is technically not their remit, the US consulate may be able to give you more information. But the authoritative source of information would be the Polish authorities, either at a consulate or at whatever service manages foreigners. Having a paper confirmation to show at passport control could be useful.

Also note that since this is specific to Poland, you wouldn't be able to travel to or through other Schengen Area countries during those 90 additional days, even in transit to/from outside the Schengen Area.

Another point is that Timatic (the database used by airlines to determine requirements for entry into various countries) does not mention this rule. Airlines are not known to count days of presence so this shouldn't be an issue, but you never know...