I got several suggestions.
     I thought it is time to answer some questions, prepare a "partial"
"quasi"- summary and give some more feedback. Please, keep sending me any
more insights and suggestions you might have.

     Briefly, the problem is:
"P622 (no systematic abscences), strong spots at h, k, l=2n and weak spots
at h,  k, l=2n+1; planes h, k, l=2n+1, the average intensity is clearly and
"much" *higher at
  high resolution than at low resolution*; off-origin Patterson peak;
refinement programs "freeze" all B-factors of a supposed  222 point group MR
solution".
     I had not mentioned that the off-origin Patterson peak is at 0, 0, and
0.5.

     Josh Waren (JW), Dale Tronrud (DT), Bart Hazes (BH) and Pierre Rizkallah
(PR) put their suggestions to the bb, Tommi Kajander (TK), Anastassis
Perraskis (AP), Esko Oksaken (EO), Peter Zwart (PZ), Robyn Stanfield (RS),
Jose Antonio cuesta-Seijo (JACS), Benajmin Bax (BB) and Xueyong Zhu (XZ)
wrote pvt messages,  I will include their comments in this summary as this
is a general practive.
JI below is me (Jorge Iulek).

TK and EO: a 2006 paper by EO "rigid body refine with weak refl and refine
with the rest later". Also, maybe try lower symmetry.
     Scale weak and strong data separately yet "assumption of independent
data is no longer valid".
     (JI): I should read the paper to check how to scale them separately; for
while my simple idea is to use rzone in mtzutils before scaling, now, with
scala.

JW: Check the suggested twinning fractions at the lower sg's, specially "a
partial twin fraction of near 0.5 _and_ perfect twinning, or if the stats
suggest partial twinning with a lower twin fraction". Particular attention
to the "l" statistic.

AP: remembers the good processing statistics at the higher resolution, so
get more resolution to facilitate
things. Possibilities are to "FeDEX" xtals to APS and ESRF.
     (JI): this will be on mind, but currently there are several difficulties
to express the protein again. The resolution was limited by instrumentation,
spot smearing and the 230 A parameters.

PZ: read about OD twins, while work with regular twin. Points an 2007 Acta D
paper.

RS: maybe a lattice translocation defect, check "if your weak spots are
smeared, and the strong spots are sharp". There a papers decribing this.
     (JI): Robyn, on eye both strong and weak spots look smeared, but
this might be subjective. I would thank you for the complete references.

DT: frozen B-factors, "ensure your bulk solvent correction is operating
correctly".
     (JI) I tried Babinet's scaling or/and bulk sovent mask with all data and
obseved the "freeze". I also cut data at 8, 6 and 5 A, no bulk solvent
model at all, I got marginally better R's, B factors slightly higher than
the floor (under refmac).

JACS: had a similar case, "due to a NCS 2-fold rotation aligned with a
crystallographic 2 fold axis". "MR
worked equally well ... refinement
would stall at terrible R values." ;
"careful trimming of the initial model .. led to a better behaved
refinement " ; "low B values are due to overfitting"
He suggests to cut away different smal parts of the structures, see the
statistics and the maps if the chuncks show up again. Also, fix Wilson B
values.

BH: suggests pseudo body centering, off-origin Patterson peak at 0.5, 0.5,
0.5.
(JI) Sorry, I added this important information only in this e-mail, it is at
0, 0, 0.5.
BH: lower symmetry with twin fraction near 0.5. Refinement may be hard even
if the crystal conditions are figured out. Additives might change pseudo to
true symmetry.
(JI) As pointed above, currently difficulties to get more protein.
BH: A wrong model that would obey the pseudo body centering would give
"good" R's and correlations. "Trying a whole bunch of rotation
function solutions and see which one will refine to a significantly lower
R-free is one thing to try"
(JI) MR was a kind of straight forward with Balbes, I can still check and
think more about the results.

BB: had a true P21 case which looked hexagonal. Calculated mine to possibly
be 114.5, 72, 229, beta=120 degrees, but wonders if this would lead more to
a screw 3-fold axis.
(JI)  Lower symmetry is a possibility I should still look better into.

XZ: guessed correctly the off-origin Patterson peak and talks about lattice
translocation, with a 2005 Acta D paper as reference. Also, talks about a
program for strong pseudo-translation.
(JI) Yes, the peak is strong, and I would like to see the program.

PR: "pacakes" of 229x229x36 A slightly shifted in the plane normal to the 6
fold, or slightly rotated out of that plane. Perturbation really small which
explain the intensity distribution profile I described.
(JI) That is my initial guess.
PR: "fix a good MR solution and use the same rotation solution (or one
very close to it) to find a second translation solution. This should be
within a small fraction of 0,0,0.5. After rigid body refinement, you
might see the rotation of the 'pancake' clearly."
"try all the screw ... 6, 6(1), 6(2), 6(3), 6(4) and 6(5)"
He also points to increasing resolution, as did AP.
(JI) AFAIU, molrep (within Balbes) uses the pseudo-translation information.
Anyway I should look into this in more detail. I wondered if the
pseudo-translation, etc..., might mess the systematic absences I
cannot observe currently.

     I hope my summary did not corrupt the ideas.
     I will be trying and testing; please, write me should you have new ideas
or suggestions.
     Thanks to all for sharing the experience.

Jorge