Probably the best description of JAXA's process is the example provided on JAXA's website of the Development of the ASCA (ASTRO-D) Project. This example is in line with JAXA's ISAS Mission Selection Procedures:
ISAS Mission Selection Procedures
ISAS has a character of an inter-university research institute, and is
run in cooperation with scientists and engineers across the nation.
Mission proposals are solicited from the team, and mission selections
are made by committees comprising about equal numbers of internal and
external members. Approved projects are then implemented with the
collaboration of scientists and engineers, again both inside and
outside ISAS.
The first stage of the mission selection is endorsement by the
Steering Committee of Space Science or the Steering Committee of Space
Engineering. Each Committee consists of about 30 members, about half
of which are from outside ISAS. The process usually starts with the
formation of a Working Group under the Committee.
Comprising scientists and engineers, the Working Group defines
objectives, identifies scientific requirements and performs
feasibility studies. When planning is complete, the Working Group
proposes the mission to the respective committee depending on the
nature of the mission. The Committee studies the proposal from various
aspects including scientific significance, technical and financial
feasibility, and maturity of the group behind the mission. When
intensive study is needed, a subcommittee is created for a detailed
assessment which sometimes results in setting priorities among
multiple proposals.
A Committee's decision to endorse a specific mission proposal is
reported promptly to the Director General. In case both Committees
endorse new missions starting in the same fiscal year, priority may be
recommended by the Director of Project Coordination.
Working Groups do not receive funds for their studies. However, the
development of hardware technologies essential for future missions is
supported by a "basic development fund" after being refereed by groups
appointed by the above Committees.
The second stage of mission selection is the decision at the Advisory
Council for Research and Development. The Council, whose 21 members
again comprise roughly equal numbers of internal and external members,
is the principal decision-making body of the Institute, and it deals
also with budgets and appointments.
The selected mission is then proposed to the government both for
mission approval by the Space Activities Commission and for budget
allocation by the Ministry of Finance. The selection process is
completed by a Diet resolution. A proposal for the new start from a
given fiscal year (which starts on April 1) must be submitted to the
government in June of the previous year.
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Hope this helps, or is at least a starting point.