I typed the following response to a thread at Sawmill Creek only to find out that I can't post there any more. (Do I need a membership?) If you're reading this and can post there, then you are welcome to send him here. No block quotes from here to there.
As stated, your main problem is that your sole is out of flat along its length. Your secondary problem is that the previous owner has convinced you that the way the profile of the iron currently matches the sole is good enough. It's not (likely).
First, 100% of un-tuned antique planes have a high spot behind their mouth. Some of them have a slight high spot and can be used, but could work better. Others are completely out of flat and don't work at all. It sounds like you have a couple of planes that fall into this latter category. (I say 100% as a joke, but I really haven't seen one that doesn't.)
That being said, the first step of tuning any antique should be to flatten the sole. Don't purchase a plane whose sole you can't flatten. I use hollows for rounds, rounds for hollows, and hollows & rounds for complex profiles. Side beads? You'll need a mother plane or an appropriately sized core router bit and router table to flatten the sole.
Side beads have a reputation as being a good plane for a beginner to start. I disagree with that mainly for this reason: flattening the sole is impossible without the correct set-up and you are probably not in possession of the correct set-up. Additionally, sharpening 180 degrees of a profile isn't the easiest place to start. Your large profiles will make both of these easier, however.
As an added bonus to flattening your sole first, you'll find matching the iron to the sole easier once the sole is flat. 1. Once flat, you won't be looking at the horizon of the bed over the mouth as you site down the sole, thinking that you're seeing the cutting edge. 2. you won't have a patina on the sole that is the same color as the silhouette of the cutting edge.
Steps to tuning antiques:
1. Avoid planes that have an ill-fitting wedge. (Cars and hand planes are similar in that any of either can be made to work flawlessly. Many of both are not worth the time, effort and expense. The fit of the wedge is a glimpse at the maker's skill and/or plane's life.)
2. Flatten sole
3. Fix mouth
4. visual inspection that iron is bedded
6. re-bed iron if the plane chatters
There's other things that can go wrong. For instance, some of those mint antiques were never used because they didn't work on the day they left the prison in which they were made. These can be avoided by skipping over ill-fitting wedges. There are integral faults in some planes from EVERY era.
Finally, I start snipes bills by striking a line with a marking gauge. I start side beads upon a square corner. You'll probably start yours with a running start.
If you have any questions then you can post them in my comments.