I haven't experienced this on my Fords, but did on a .....dare I say...a 396 and 454 Bowtie! Yikes - I just said the C word!


My brother is a big Chevy guy - go figure - but did result in some great Bench racing as teens.
Using stock valve train with a high lift cam commenly causes the issue you are seeing - especially if all the parts are not brand new.
Here is what I would recommend - use at your own discretion....
1) you definitely need screw in studs - if you don't have them the high lift on the cam will pull the pressed in ones out. 2) get some good aftermarket roller tip rocker arms - WELL worth the money. 3) swap out the stock springs - you can do it with the heads on the car - find the correct tool at the local AutoZone - put the piston at TDB - and you will be fine swaping out the springs. 4) USE HARDENED push rods and retainers - don't scrimp here and don't assume what you have is good. If you have broken an arm it is very likely you have bent a push rod (probably most of them are bent by now).
OR you could go the other way and pull out the cam and swap it for a more reasonable one. Most novices make the mistake of putting a wild cam in to get the lumpity/lump and forget that all the other pieces need to match for it to work reliably.
It will definetly be worth the money in the long run - and doesn;t require a machine shop (except thescrew in studs) or full motor rebuild. Plus it will be a great weekend project - maybe two.
Good luck.