Here, as always, it would improve the quality of answers and comments, if operating data, even approximately, were known.
Some comments to your questions:
A) I read in this case integrity as 'of proven good reliable standard over lifetime / made by good workmanship'. I agree with littleinch to ask your customer to qualify: for instance also proven over time at exact same application, references over time, expected periode in operation without repair, cost of repair and spares to compare lifetime cost.
B) Lifetime cost, included cost of downtime and repair could well be lower than competitive other types of valves.
C) Good quality non-slam axcial check valves will have very low headloss. Under circumstances this could add considerably to economy if fluid is pumped.
D) Good quality axcial non-slam valves could under circumstances be dimensioned with lower diameter (higher flow-speed) than competiting valves of other types and lower than pipeline diameter, and still at lower headloss, also contributing to economy.
E) For water handling and some neutral fluid add make Erhard (Germany) to your list, others than mentioned above exists on market.
Good luck!