I have no experience in using the EFP feature in GAMESS. I suggest:
(1) Check if the wavefunction generated with EFP can be properly loaded into Multiwfn. Please check section "6.5 Check sanity of wavefunction" of Multiwfn manual.
(2) Plot electron density difference (EDD) between the wavefunction with and without the presence of EFP, and check if the EDD makes sense (i.e. properly reflecting the polarization effect caused by EFP). Please check Section 5.5 of Multiwfn manual on how to plot isosurface map of EDD.

If the above tests can be successfully passed, then you can normally perform other analyses on the wavefunction generated with EFP, including calculating electronic spatial extent.

How is the electronic spatial extent computed when using GAMESS with the EFP model included? The values obtained with and without the EFP model seem very different using Multiwfn features, so I would like to understand how this is calculated and whether the difference makes sense.

I have included my input as a reference:

$contrl scftyp=rohf runtyp=ENERGY ICHARG=-1 MULT=2 $end                                                                                                                                                                                                                                                                                                                                                                             
$GUESS GUESS=HCORE $end
$system timlim=999999100 mwords=1500 $end
$data
point
C1
X   0.0      0.00000   0.00    0.0000000000
S 1
1   1.60      1.0
S 1
1   0.54      1.0
S 1
1   0.18      1.0
S 1
1   0.06      1.0
S 1
1   0.02      1.0
S 1
1   0.007     1.0
S 1
1   0.0025    1.0
P  1
1   0.54      1.0
P  1
1   0.18      1.0
P  1
1   0.06      1.0
P  1
1   0.02      1.0
P  1
1   0.007     1.0

$end

$EFRAG
COORD=CART POSITION=OPTIMIZE
FRAGNAME=H2ORHF !  1
O1  0.8194151  3.761265799  1.463524578
H2  1.25703299  3.576098096  0.608074709
H3  1.280316821  3.151610025  2.091123223
FRAGNAME=H2ORHF ! 2
O1  3.235309493  0.323789516  0.826027175
H2  2.287042643  0.245318854  0.545046148
H3  3.49739612  -0.607746132  1.015819479
FRAGNAME=H2ORHF !  3
O1  2.120318615  1.829099822  3.067825523
H2  2.716737776  1.429997077  2.403073423
H3  1.393682966  1.16456958  3.094789951
FRAGNAME=H2ORHF !  4
O1  1.678625202  2.668205407  -1.097398397
H2  1.313270863  1.8116964  -0.7541709
H3  0.97946341  2.950928994  -1.722548322
FRAGNAME=H2ORHF !  5
O1  4.031544555  1.1824368  -1.782829834
H2  3.329476315  1.864006148  -1.759136145
H3  3.976510312  0.836686535  -0.865085531
FRAGNAME=H2ORHF !  6
O1  -0.951816539  2.868496127  -2.329524882
H2  -1.073959051  2.769723797  -1.362605656
H3  -0.725286019  1.94939685  -2.613578646
FRAGNAME=H2ORHF !  7
O1  2.444206884  -0.836139287  -3.02613159
H2  3.054631981  -0.161539045  -2.645099687
H3  2.256873915  -1.43762867  -2.278819197
FRAGNAME=H2ORHF !  8
O1  -0.163312655  0.187848718  -2.667647072
H2  0.754775342  -0.071596002  -2.937345617
H3  -0.140401135  0.077193627  -1.667876295
FRAGNAME=H2ORHF !  9
O1  -1.401793316  2.294204052  0.60887374
H2  -0.932104766  1.425927566  0.407864754
H3  -0.687430812  2.866389123  1.002229255
FRAGNAME=H2ORHF !  10 
O1  3.699576882  -2.47709352  1.109367592
H2  3.131463416  -2.685382029  1.871420207
H3  3.072805134  -2.577208463  0.361498585
FRAGNAME=H2ORHF !  11 
O1  -2.445224889  0.836599263  3.025611356
H2  -3.055175811  0.161613278  2.644465732
H3  -2.257656722  1.437882093  2.278218062
FRAGNAME=H2ORHF !  12 
O1  0.95210556  -2.868100705  2.330332258
H2  1.074165811  -2.769001232  1.363469437
H3  0.725794887  -1.949092547  2.614729384
FRAGNAME=H2ORHF !  13 
O1  0.162391343  -0.187435567  2.668727583
H2  -0.755763142  0.072558403  2.937769271
H3  0.139998853  -0.077701929  1.668796296
FRAGNAME=H2ORHF !  14 
O1  -3.699591074  2.47636163  -1.111380942
H2  -3.13013588  2.684536198  -1.872496966
H3  -3.074228044  2.576788566  -0.362486324
FRAGNAME=H2ORHF !  15 
O1  1.402520332  -2.294147933  -0.609652451
H2  0.932213602  -1.426286264  -0.407941841
H3  0.68812406  -2.86721981  -1.001742925
FRAGNAME=H2ORHF !  16 
O1  -4.031865681  -1.182964379  1.782579242
H2  -3.329245916  -1.86401444  1.758853929
H3  -3.97703888  -0.837156789  0.864855572
FRAGNAME=H2ORHF !  17 
O1  -1.678116086  -2.6672484  1.097288746
H2  -1.312613874  -1.810461014  0.754694558
H3  -0.979443835  -2.950249964  1.722833194
FRAGNAME=H2ORHF !  18 
O1  -3.235616469  -0.32432914  -0.826347925
H2  -2.287511055  -0.245495298  -0.544943741
H3  -3.497831686  0.607048253  -1.016662792
FRAGNAME=H2ORHF !  19 
O1  -0.819056265  -3.761496007  -1.46199334
H2  -1.257084495  -3.574907723  -0.607000601
H3  -1.278522735  -3.151485695  -2.090262866
FRAGNAME=H2ORHF !  20 
O1  -2.119810012  -1.829436025  -3.067565147
H2  -2.715554922  -1.430332226  -2.402179383
H3  -1.393276171  -1.164793559  -3.09513136
$END