Thanks for everyone's input so far.
I set up this poll to get some idea of what everyone's experiences have been. Personally, I've never done anything on the hydraulic side of the system before and am starting to realize - partly from reading the advice here - that it isn't something that should be ignored. I'm also realizing that it should be something I can easily do myself.
LarryBible raised the question of cost between Speedbleeders and a Powerbleeder which is certainly a consideration that I have been debating. From what I can see, the speedbleeders run $7 each plus $3 S&H or $31 for one car and $28 for each additional car (if you order all at once to minimize shipping). The Powerbleeder starts at $~50 but you may end up having to purchase multiple adapters to fit different vehicles. Right now I have three cars to consider which would need two adapters according to the PowerBleeder website. I'm waiting for them to get back to me with the total package price.
'87 560SEL 267K (177K on motor) Blue/Blue
'98 Buick LeSebre 60K (wife's car)
'56 Imperial Sedan 124K
'67 Dodge Monaco 130K (Sold)
'87 Chrysler 5th Ave 245K and going strong (sold)
'73 Plymouth Satillite 175K (sold)
'96 Chrysler LHS 80K (totaled)