Dear Bob,
The manufacturer's recommendation is to replace the barrel complete. Having said that, buying a 20dollar part (+shipping in my case) for a 20 dollar watch is not economically sound unless you're going for a rebuild of a watch which has high value (chrono, vintage diver). Some Swiss high-beat movements used sealed mainsprings, in these cases since the value of the watch may be higher and to achieve the accuracy it was designed for it is worth spending the money on a new barrel/spring.
In most of the cases with the Seiko barrels/springs, I have found that that the lubricant has deteriorated to the extent that it serves no purpose and may even hinder the correct function of the watch.
I agree with you that the barrel cover is flimsy. It gets its strength through the rigidity offered by the large lip around its circumference, rather than other watches where the cover itself is quite thick. To avoid distorting the cover, pry it up just a little bit and work your way around. Don't try to get it off in one go.
One reason that i usually open the barrels on these Seikos is that they use one bridge for both train and barrel. If you suspect that the mainspring is giving problems then you have to remove everything from the balance onwards. Unlike in most Swiss watches where the barrel can be removed without disturbing the other stuff.
To avoid getting all that black stuff all over your desk, open the barrel and rinse it in some other fluid.. thinner or even WD-40 to get the worst of it off. I usually soak it for a few minutes in thinner.. (beware of flames, no smoking etc...)
Anil