Is there any prohibition to having base agreements and awarding task / project orders to these holders?
The requirements for competition are not the same as they are for Government contracts. Specifically,
CFR Title 32 SUBCHAPTER C-DoD GRANT AND AGREEMENT REGULATIONS, PART 21 Subpart C—Competition states:
General policy and requirement for competition.
(a) It is DoD policy to maximize use of competition in the award of grants and cooperative agreements. This also conforms with:
(1) 31 U.S.C. 6301(3), which encourages the use of competition in awarding all grants and cooperative agreements.
(2) 10 U.S.C. 2374(a), which sets out Congressional policy that any new grant for research, development, test, or evaluation be awarded through merit-based selection procedures.
(b) Grants officers shall use merit-based, competitive procedures (as defined by § 22.315) to award grants and cooperative agreements:
(1) In every case where required by statute (e.g., 10 U.S.C. 2361, as implemented in § 22.310, for certain grants to institutions of higher education).
(2) To the maximum extent practicable in all cases where not required by statute.
In other words, unless your situation is specifically covered by statute (which I cannot know), competition requirements apply "to the maximum extent practicable." The basis for lack of competition in your situation should be documented and approved at a sufficiently high level, which may depend on the USACE's specific procedures for cooperative agreements. The DoD IG report at this link also provides information on competition expectations for cooperative agreements in the USACE.