I'd avoid average cost basis. You're better off deciding which lots to sell when the time comes so you can decide which lot best meets your needs. If you're in a low tax bracket, you may want to sell shares that have appreciated a lot. If you're in a higher bracket or want to try and keep your income under a certain amount (ie. for ACA subsidies) it may be better to sell shares that have less gains. The average basis does not give you the same flexibility. If you ever want to donate shares to a charity (either directly or through a Donor Advised Fund), it's also much more advantageous to be able to pick the most appreciated shares since you/the charity do not pay taxes on the gains and you can still deduct the full amount if you itemize.
Another thing to consider is that FZROX is probably not the best choice for a taxable account.
First, mutual funds are generally not as tax efficient as ETFs. Vanguard is the exception at the moment since they link many of their mutual funds to an ETF. For example, I just converted VTSAX to VTI and kept the same cost basis. They're basically equivalent, just different forms. There's a patent for this that is expiring soon I believe, and other places may copy it. But in general, mutual funds may incur more capital gains than ETFs each year, which you have to pay taxes on. You can research this more, but there's a lot of info out there about how ETFs are more tax efficient than mutual funds.
Second, FZROX in particular is a mutual fund specific to Fidelity. I don't believe you can hold it with any other brokerage. So if for some reason, you decide you want to transfer to a different broker, you'd need to sell the FZROX and pay taxes on any gains. For most other mutual funds and definitely ETFs, you can transfer in kind and keep your cost basis with the new broker. I like Fidelity now too, but I like to keep my options open rather than be stuck with them.
FZROX is certainly not a terrible choice, but I'd recommend putting any new money into an ETF like VTI. With another great year of gains, it's probably not worth selling the FZROX at this point. I'd maybe try to reinvest dividends into the new ETF if you can rather than into FZROX. But yes, you should reinvest dividends unless you need the money for something. It's not really more complicated, it just adds more lots. That's not really a bad thing, just more to keep track of, which Fidelity does for you. For many years, I invested weekly into VTSAX at Vanguard, like $150-200 a week. This means I have a ton of lots. In hindsight, I probably could've just done once a month and avoided many of the extra lots and it wouldn't have changed things much. I wanted to avoid buying at the worst time and justified spreading it out because of this. It kept me investing which is the important thing. So compared to my 52 lots per year, I wouldn't worry too much about 4 lots per year (assuming quarterly dividends)!