Groebner basis computation extremely slow

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I wanted to compute the elimination ideal of some ideal. When I call elimination_ideal, it is unacceptably slow (+10 min), and when I tried to first compute the Groebner basis by hand then extract the elimination ideal, it is also very slow (+10 min).

Not sure what's wrong:

R2.<q10, q11, q12, q13, q14, q20, q21, q22, q23, q24, p,p0, p1, p2, p3, p4> = PolynomialRing(QQ,order = 'lex(11),lex(5)')
R2.inject_variables()
M1=Matrix([[q10,q11/4,q12/6,q13/4],[q11/4,q12/6,q13/4,q14]])
M2=Matrix([[q20,q21/4,q22/6,q23/4],[q21/4,q22/6,q23/4,q24]])
I1=R2.ideal(M1.minors(2))+R2.ideal(q10+q11+q12+q13+q14-1)
I2=R2.ideal(M2.minors(2))+R2.ideal(q20+q21+q22+q23+q24-1)
graph_ideal=[p0-p*q10-(1-p)*q20, p1-p*q11 - (1-p)*q21, p2-p*q12-(1-p)*q22, p3-p*q13-(1-p)*q23,p4-p*q14-(1-p)*q24]
J=I1+I2+R2.ideal(graph_ideal)
Jgb=J.groebner_basis()

Then my computer just froze there for a good 10-ish min. I tried to switch different backends (libsingular:std, linsingular:slimgb, macaulay:gb), and they both just stop right there.

I want to know if it is something I did wrong, or it is just a very hard example to compute. If it is the latter situation, is there any way to allow GPU acceleration or just multi-threading in this situation?

As a reference, I also tried this computation with the following code on Macaulay2, and it seems to handle it with ease:

R2 = QQ[q10,q11,q12,q13,q14, q20,q21,q22,q23,q24, p,p0,p1,p2,p3,p4, MonomialOrder => Eliminate 11];
M1 = matrix{{q10, q11/4, q12/6, q13/4},{q11/4, q12/6, q13/4, q14}};
I1 = ideal(q10 + q11 + q12 + q13 + q14 -1) + minors(2, M1);
M2 = matrix{{q20, q21/4, q22/6, q23/4},{q21/4, q22/6, q23/4, q24}};
I2 = ideal(q20 + q21 + q22 + q23 + q24 -1) + minors(2, M2);
I3 = ideal(p0 - p*q10 - (1-p)*q20,p1 - p*q11 - (1-p)*q21,p2 - p*q12 - (1-p)*q22,p3 - p*q13 - (1-p)*q23,p4 - p*q14 - (1-p)*q24);
J = I1 + I2 + I3;
gens gb J