OK you asked .. I play almost exclusively at $200 mil so here are some of my opinions.
It is the most isolated set, basically the top 300 players, so you don’t need to study lower priced bargains. Also ballparks are usually more bomber slanted (all I play are big parks or heavily slanted).
Draft a team for your park. Plan for platoons .. you should have at least 4 or more. In that way you are drafting based on half cards, meaning best first baseman might be Foxx, but that Cash / Hodges can be better than Gehrig.
Even in Minutemaid platoons are important, I believe players like McGwire, Hartnett, Guerrero, Clark and my personal favorite Ron Santo are key as they can platoon and give an advantage against RHP.
Learn from post draft analysis, who were your replacements? What LH hitters are on Minutemaid Teams? What RH are in LH parks. The means they were not listed on anyones card .. such as your Beckwith example .. next draft you may want to list him as 20th or something like that .. understanding he is usually a top 5 pick. Look at players with only one high priced card as potential “flyers” to list lower on your card. Gibson, Beckwith, Wells all come to mind.
A few examples .. my latest team .. and corresponding draft list (note I got Gibson at 15)
http://onlinegames.strat-o-matic.com/team/8221911. Mantle, Mickey (1956) (CF) - 13.97M
2.Vaughan, Arky (1935) (SS) - 10.20M
3.Morgan, Joe (1976) (2B) - 10.30M
4.Brett, George (1982) (3B,LF) - 6.15M
5.Mathewson, Christy (1909) (P) - 10.55M
6.Hoffman, Trevor (1998) (P) - 5.85M
7.Gonzalez, Juan (1992) (CF,LF) - 3.45M
8.Jones, Chipper (1999) (3B,SS) - 9.71M
9.Allen, Dick (1964) (3B) - 5.29M
10.Dickey, Bill (1937) (C) - 7.77M
11.Cash, Norm (1968) (1B) - 2.67M
12.Chance, Dean (1967) (P) - 6.83M
13.Taylor, Jack (1900) (P) - 6.44M
14.Gibson, Josh (NeL) (C,LF,1B,RF) - 13.69M
15.Maris, Roger (1961) (RF,CF,LF) - 9.52M
16.Stargell, Willie (1972) (1B,LF) - 4.84M
17.Wagner, Billy (1999) (P) - 5.78M
18.Fryman, Woodie (1980) (P) - 4.25M
19.Bonds, Barry (2001) (LF) - 14.54M
20.Bender, Chief (1910) (P) - 9.64M
21.Keefe, Tim (1888) (P) - 9.42M
22.Brown, Three Finger (1906) (P) - 9.44M
23.Kiner, Ralph (1950) (LF) - 6.64M
24.Nathan, Joe (2006) (P) - 4.73M
25.Ramirez, Manny (2000) (RF) - 7.99M
And my only championship team and draft list ..
http://onlinegames.strat-o-matic.com/team/8151761.Ruth, Babe (1916) (P) - 8.66M
2.Mantle, Mickey (1956) (CF) - 13.97M
3.Morgan, Joe (1976) (2B) - 10.30M
4.Schmidt, Mike (1977) (3B) - 7.92M
5.Adams, Babe (1915) (P) - 6.14M
6.Larkin, Barry (1996) (SS) - 10.88M
7.Wagner, Billy (1999) (P) - 5.78M
8.Bagwell, Jeff (1994) (1B,RF) - 11.60M
9.Thomas, Frank (1994) (1B) - 11.44M
10.Hoffman, Trevor (1998) (P) - 5.85M
11.Tiant, Luis (1976) (P) - 4.17M
12.Allen, Dick (1964) (3B) - 5.29M
13.Wood, Joe (1920) (RF,CF) - .91M
14.Bonds, Barry (2001) (LF) - 14.54M
15.Gibson, Josh (NeL) (C,LF,1B,RF) - 13.69M
16.Vance, Dazzy (1934) (P) - 1.99M
17.Foxx, Jimmie (1932) (1B,3B) - 13.16M
18.Jackson, Reggie (1982) (RF) - 3.79M
19.Thome, Jim (1996) (3B) - 7.91M
20.Brown, Three Finger (1906) (P) - 9.44M
21.Joss, Addie (1906) (P) - 8.93M
22.Piazza, Mike (1997) (C) - 9.93M
23.Alomar, Roberto (1992) (2B) - 7.49M
24.Fryman, Woodie (1980) (P) - 4.25M
25.Miller, Stu (1957) (P) - 1.74M
Finally a Minutemaid team still in progress
http://onlinegames.strat-o-matic.com/team/8176001.Dimaggio, Joe (1941) (CF) - 11.63M
2.Lajoie, Nap (1901) (2B,SS) - 10.64M
3.Thomas, Frank (1994) (1B) - 11.44M
4.McGwire, Mark (1998) (1B) - 11.09M
5.Larkin, Barry (1996) (SS) - 10.88M
6.Tiant, Luis (1976) (P) - 4.17M
7.Eckersley, Dennis (1990) (P) - 5.34M
8.Hartnett, Gabby (1930) (C) - 8.18M
9.Henderson, Rickey (1982) (LF,CF) - 5.32M
10.Brown, Three Finger (1908) (P) - 10.39M
11.Rodriguez, Alex (2005) (3B,SS) - 10.33M
12.Allen, Dick (1966) (3B,LF) - 7.88M
13.Chance, Dean (1964) (P) - 9.14M
14.Taylor, Jack (1902) (P) - 9.18M
15.Santo, Ron (1970) (3B,LF) - 3.89M
16.Guerrero, Vladimir (2002) (RF) - 9.73M
17.Ramirez, Manny (2000) (RF) - 7.99M
18.Winfield, Dave (1979) (RF,CF) - 8.36M
19.Smith, Dave (1987) (P) - 5.34M
20.Nathan, Joe (2006) (P) - 4.73M
21.Mossi, Don (1954) (P) - 4.72M
22.Medwick, Joe (1934) (LF,RF) - 4.36M
23.Bench, Johnny (1970) (C,1B,3B,LF,CF) - 7.59M
24.Joss, Addie (1908) (P) - 10.19M
25.McLain, Denny (1969) (P) - 6.19M
Hope it gives you some insight .. and encourages you to try another at $200