That 7% growth rule is doing a lot of analytical work in the screen. Easier for Buffett, I'm sure, but a very hard ask for mere mortals.

Indeed.
The thing is you want that growth even in the "pretty darned bad" scenarios, which means you have to understand the business well enough to understand what the various outcomes might be, and their probabilities.
So all you can do with a database is create plausible nominees.

But, FWIW, here is a list which meets all the following criteria, as a hunting ground.
* In the ~1600 stocks currently covered by Value Line
* EPS growth last 5 years > 7%
* Forecast EPS growth next 3-5 years > 7%
* Earnings yield indicates P/E < 15, using ALL of the following: trailing EPS, "current" EPS, forward EPS, est current fiscal EPS, and est next fiscal EPS.

Sorted in decreasing order of lowest of those earnings yields. i.e., "cheapest" first.
There are 147 of them.
This is done using data from Friday before last.

There are two lists below. First one is 147 stocks as described. Way down at the bottom is the same list, but requiring >11% trailing and forward EPS growth rates---think of that as 7%/year growth plus 4%/year inflation. There are 56 of them.

ABG
TOL
TGNA
DINO
GPI
EWBC
PHM
WBS
AN
RF
TS
CNHI
HWC
MTG
TEX
DDS
ASIX
HBAN
ONB
MFC
ALLY
ARCH
ALSN
GES
NMIH
BERY
AGCO
BC
HPQ
SANM
FCF
ARW
BLDR
WCC
AXS
AMG
OXM
BYD
JPM
AMWD
DVN
HRI
DKS
DAR
VSH
OC
MET
OLN
CFR
OVV
SWN
HIG
BABA
FMC
MPLX
PLAB
WKC
CLS
WES
URI
AFG
CMCSA
DOOR
JACK
SON
STLD
ATSG
CNC
IMO
CMCO
FLEX
TRP
ADM
SSNC
IART
HI
TTMI
MKL
AIG
GL
CVX
GHC
SLGN
DE
FRO
SEE
LKQ
G
MCHP
SF
IPG
WEX
RRX
CMI
BLD
RS
AVNS
SPH
SHEL
CHTR
MS
AMP
HCA
IBP
NTAP
TRU
AMKR
NXPI
DIOD
BOOT
LOW
MCRI
ACGL
CI
ELV
AMX
FLT
SNA
EPC
AFL
BECN
GPC
PRI
WRB
PYPL
SEM
SIRI
VMI
IBKR
ALLE
KEYS
TGT
KMI
SEDG
AWI

Second list, 56 stocks requiring 11%/year trailing and forward estimate EPS growth rates
TOL
DINO
GPI
AN
TS
CNHI
TEX
ALSN
GES
NMIH
BLDR
WCC
BYD
HRI
DAR
OC
STM
OVV
SWN
PLAB
WKC
DOOR
IMO
MKL
CVX
DE
G
SF
WEX
RRX
BLD
AVNS
SPH
SHEL
CHTR
AMP
IBP
CAT
MCRI
ACGL
CI
ELV
FLT
EPC
WRB
PYPL
SIRI
VMI
KMI
SEDG