Welcome to the club. One of my ancestors came to the USA as Heinrich Kesselberg and died Henry Casselberry. He and his sons used one from list "A" and one from list "B" in every combination during their lives
A:
---------
Kessel
Cassel
Castle
B:
---------
berry
bury
berg
burg
I have found Pack relatives as Pack, Park, Peck, Pick, Pock, Puck, Pok and Pork.
If people spelled consistently the sport would be as boring as "fishing" at a trout farm - the places that feed the fish until they weigh 10 - 14 pounds, then put them out in the public pool and stop feeding them. You pay by the pound and they guarantee you'll catch something, usually on the first cast.
"Totally different" would be a change from "Zimmerman" to "Carpenter" during the anti-German fervor around World War I. ("Zimmerman" is German for "Carpenter".)
How you try is the same as anyone; one generation at a time, verifying as you go. Any genealogical search engine worthy of the name has a soundex option. It is the default on the LDS mega-site. You have to select it in Roots Web and Ancestry.
As an example of my own success (brag, brag, brag), I was hunting for Henry Monebrake and his wife Catherine in the 1880 census.
I found them, after trying:
1) Henry Monebrake
2) Henry Moneybrake
3) Catharine Monebrake
4) Catharine Moneybrake
5) Henry Monebraker
6) Henry Moneybraker
7) Catharine Monebraker
8) Catharine Moneybraker
9) Monebroke
10) Moneybroke
11) Monebroker
12) Moneybroke
13) Moneybroker
14) All Catharine (regardless of surname) in Ohio with birth year 1800 - 1820 and head of household Henry
15) All Henrys in Preble county born in Germany 1800 - 1820
My 16th try was any Catherine in Preble County (regardless of surname) born in Germany 1800 - 1820. I found them in Washington Twp, Preble, Ohio:
(Name, Relation, Marital Status, Gender, Race, Age, Birthplace, Occupation, Father's Birthplace, Mother's Birthplace)
Harry Monnebraker, self, M, Male, W, 74, Pr, Farmer, Pr, Pr,
Catherine Monnebraker, wife, M, Female, W, 64, Ger, Keeping House, Ger, Ger
Have fun!