Dividend reinvestment = tax nightmare?

Background: A small sum was put up for me when I was a child. It was supposed to be used to cover college expenses, but we never liquidated it. I asked my folks if they’d like it to cover what they contributed, but they said to keep it. I’ve not been diligent about dealing with it other than collecting the 1099 each year for my tax return. Since it’s not invested aggressively enough for my taste (it’s a bond fund,) I want to reallocate. That means selling the shares, and I’m worried about the tax nightmare that this will unleash. Apparently this account has been transferred a few times during mergers and sales. It’s now with MSSB, and they have no idea what the tax basis is, and I don’t have records for the >20 years the dividends were reinvested. All of my other investments are in tax-deferred and pre-tax accounts, so I’ve never had to deal with this.

My questions:
How do I best handle this sale on my Schedule B? Have any of you ever had to deal with this? I can make an educated guess, and I imagine that it’ll be pretty accurate since bond fund prices don’t seem to bounce around all that much, but I neither want to pay way too much nor piss off the feds. Is automatic reinvestment more trouble than it’s worth for taxable accounts?

I have no pressing need to keep this money with MSSB. They gave me a spiel about putting the money into a actively managed account that charges me 1.5%/year. I’m assuming that’s on top of the the expense ratios that are included for any funds they purchase with my money. That smells a little to me, considering there are passively managed funds out there with expense ratios <0.1%. I suspect that if I’m just looking to buy a spread of passively managed funds, I may just be better off transferring everything to a discount broker and working with them. That’s a little more initial hassle though. Thoughts?

Looks like I threw this one right off the deep end. Surely some of you must invest in taxable accounts. Is dividend reinvestment the nightmare it seems to be?